essays on power system economics 04-19-10
TRANSCRIPT
Essays on Power System Economics
Dissertation
By
Sompop Pattanariyankool
May 2010
Tepper School of Business
Carnegie Mellon University
Pittsburgh, PA 15213
Dissertation Committee:
Lester B. Lave (Chair)
Jay Apt
Keith Florig
Marvin Goodfriend
Submitted in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Economics.
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Abstract
Chapter 1: Optimizing Transmission from Distant Wind Farms
We explore the optimal size of the transmission line from distant wind farms,
modeling the tradeoff between transmission cost and benefit from delivered wind power.
We also examine the benefit of connecting a second wind farm, requiring additional
transmission, in order to increase output smoothness. Since a wind farm has a low
capacity factor, the transmission line would not be heavily loaded, on average; depending
on the time profile of generation, for wind farms with capacity factor of 29-34%, profit is
maximized for a line that is about ¾ of the nameplate capacity of the wind farm.
Although wind generation is inexpensive at a good site, transmitting wind power over
1,000 miles (about the distance from Wyoming to Los Angeles) doubles the delivered
cost of power. As the price for power rises, the optimal capacity of transmission
increases. Connecting wind farms lowers delivered cost when the wind farms are close,
despite the high correlation of output over time. Imposing a penalty for failing to deliver
minimum contracted supply leads to connecting more distant wind farms.
Chapter 2: The optimal baseload generation portfolio under CO2 regulation and
fuel price uncertainties
We solve for the power generation portfolio that minimizes cost and variability
among existing and near-term baseload technologies under scenarios that vary the carbon
tax, fuel prices, capital cost and CO2 capture cost. The variability of fuel prices and
uncertainty of CO2 regulation favor technologies with low variable cost and low CO2
emission. The qualitative results are expected; stringent CO2 regulation cost leads to
more technology with little carbon emissions, such as nuclear and IGCC CCS, while
penalizing coal. However, the variability of fuel prices and the correlation among fuel
prices are the principal attributes shaping the optimal portfolio mix. We also model a
Bayesian approach that allows the planner to express his belief on the future cost of
power generation technology.
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Acknowledgements
I thank the Royal Thai Government for all the financial support. Also the staffs at the Office of Educational Affair, Royal Thai Embassy at Washington D.C. help me with many issues. I thank the Ministry of Energy Thailand for giving me an opportunity to study here. I would like to express the deepest gratitude to my advisor, co-author of my papers and committee chair, Lester B. Lave. He gives me an opportunity to work on the field that I am interested in. He is always available when I need help and guidance. He also teaches me many things not only valuable for the research but also for my life. This dissertation would not have been possible without him. I would like to thank my dissertation committees. Jay Apt helps me with many issues. The excellent wind data he provided helped me in formulating the study on wind transmission investment. He also gives the critical comments that help improving my research. Marvin Goodfriend gives me useful advice on my research and research presentation. Keith Florig gives me useful comments and idea for my research. I am thankful to the faculties who taught the PhD courses. They give me a chance to learn many advanced economics and financial economics lessons. I am grateful to my family; my parents, sister, brother and my aunts. They give me strength to finish my PhD in a place thousands miles away from home. They have supported me for my whole life. I also thank my girlfriend for her love, encouragement and patience. I thank all my friends in Pittsburgh for helping me settling my life here and making life enjoyable. In addition, I would like to thank Lawrence Rapp for all his help since the day I applied to the school.
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Chapter 1 Optimizing Transmission from Distant Wind Farms
1. Introduction
California and 29 other states have renewable portfolio standards (RPS) that will
require importing electricity generated by wind from distant locations. A long
transmission line increases cost significantly since its capacity factor is approximately the
same as the wind farms it serves, unless storage or some fast ramping technology fills in
the gaps left by wind generation. We explore issues surrounding importing wind
electricity from distant wind farms, including: the delivered cost of power, considering
both generation and transmission, the cost of the transmission line, when to pool the
output of two wind farms to send over a single transmission line, and what additional
distance would the owner be willing to go for a better wind site in order to minimize the
cost of delivered power.
Wind energy is the cheapest available renewable at good wind sites. Since no fuel
is required, generation cost depends largely on the investment in the wind farm and the
wind characteristics (described by the capacity factor). Assuming $1,915/kW for the cost
of the wind farm, annual operations and maintenance (O&M) costs of $11.50/kW-yr,
variable O&M cost of $5.5/MWh, a blended capital cost of 10.4%, and a 20 year life time
for the turbine, generation costs at the wind farm are around $76/MWh, $66/MWh,
$59/MWh, $56/MWh, and $53/MWh, respectively, for the wind farms with capacity
factors of 35%, 40%, 45%, 47.5%, and 50%, respectively.
Wind is the fastest growing renewable energy, adding 8,558 MW of capacity in
2008, 60% more than the amount added in 2007 (Wiser and Bolinger, 2009). Total wind
capacity in 2008 was 25,369 MW, about 2.2% of U.S. total generation nameplate
capacity.
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Good wind sites (class 4-6 with average wind speed 7.0-8.0 m/s at 50 m height
(AWEA, 2008)), accounting for 6% of the U.S. land, could supply 1.5 times current U.S.
electricity demand (DOE, 2007). However, transmission is a key barrier for wind power
development, since good wind sites are generally remote from load centers (DOE,
2008a). The low capacity factor of a wind turbine, added to the remoteness of good wind
sites, makes transmission a major cost component. Denholm and Sioshansi (2008) note
that transmission costs can be lowered by operating the transmission line at capacity
through storage or fast ramping generation at the wind farm. Whether this co-location
lowers the delivered cost of electricity depends on the site characteristics and other
factors.
Low utilization of a long transmission line could double the cost of delivered
wind power, since a wind turbine’s capacity factor is only 20-50%. Using actual
generation data from wind farms, we model the optimal capacity of a transmission line
connecting a wind farm to a distant load. We show that the cost of delivered power is
lowered by sizing the transmission line to less than the capacity of the wind farm.
We assume the wind farm is large enough to require its own transmission line
without sharing the cost with another wind farm or load in a different location. While we
know of no example of a wind farm building its own transmission, T. Boon Pickens
proposed to do this. If 1,000 MW were to be sent 1,000 miles or more, available capacity
in short, existing lines would not be helpful. We also extend the model to two wind
farms, trading off the additional transmission needed to connect the farms against the less
correlated output. The relationship between wind output correlation and distance is
modeled using the wind data from UWIG (2007). Finally, we model the effect of
charging wind farms for failing to provide the minimum supply requirement.
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2. Model
2.1 One Wind Farm Model
In this model, a wind farm is large enough to require its own high voltage DC
transmission line to the load. The project consists of the wind farm and transmission line.
We formulate the model as the owner of the wind farm and transmission line seeking to
maximize profit. However, in this case the objective function is equivalent to seeking to
maximize social welfare, as explained below.
The general form of the objective function for optimizing the capacities of the
transmission line is: 40
21 200 1 1 1
min[ , ] ( )(1 ) (1 )
Nji
jijs j i
p WCMAX NPV q sK aC sK WCr r≤ ≤
= =
= − − −+ +∑∑
K = capacity of the wind farms (MW)
s = transmission capacity normalized by total capacity of the wind farm (called
“transmission capacity factor”)
a = length of the transmission line (mile)
( )C sK = cost per mile of sK MW transmission line built in year 0
i = ith hour in a year
j = jth year (from 1st – 40th)
N = 8,760 hours in a year
jip = the expected price of wind power ($/MWh) in year j at hour i
jiq = the expected delivered wind power (MWh) in year j at hour i
r = the discount rate
1WC = cost of the wind turbines built in year 0
2WC = cost of the wind turbines built in year 20
The lifetimes of the transmission line and wind turbine are assumed to be 40 and
20 years respectively. Thus, the turbines must be replaced in year 20. We also assume
that construction is instantaneous for both transmission and turbines.
Transmission investment has economies of scale over the relevant range; the cost
per MW decreases as capacity of the line increases (Weiss and Spiewak, 1999). Line
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capacity is defined as the “thermal capacity” in megawatts (MW) (Baldick and Kahn
(1993)). The transmission line cost is C(q) per mile, where q is the capacity of the line.
C(q) is increasing and concave, )(' qC ≥ 0 and )('' qC ≤ 0.
We assume no line loss (delivered power equals the injected amount) and the wind
distribution (output) is the same in all years.
According to Barradale (2008), about 76% of wind power is purchased via a long term
power purchasing agreement (PPA) that specifies a fixed price or price adjusted by inflation.
Electricity price paid to the wind farm is assumed to be constant over time and unrelated to the
quantity of wind power supplied. Thus, whether the owner seeks to maximize profit or a
public authority seeks to maximize social welfare, the goal is to maximize the benefit of
delivered wind power by optimizing the size of the transmission line.
Given these assumptions, the variables iq and P are used instead of jiq and jip to
represent the constant annual output and fixed price. The optimization problem is
simplified as follow.
( )40
21 200 1 1 1
1 min[ , ] ( )(1 ) (1 )
N
ijs j i
WCMAX NPV P q sK aC sK WCr r≤ ≤
= =
⎛ ⎞= − − −⎜ ⎟
+ +⎝ ⎠∑ ∑
Let 40
1
1(1 ) j
j rβ
=
=+∑ , ( )
1min[ , ] ( , )
N
ii
q sK Q s K=
=∑ and 21 20(1 )
WCWC WCr
+ =+
.
The above objective function can be written as;
0 1 ( , ) ( )
sMAX NPV PQ s K aC sK WCβ
≤ ≤= − −
The optimal transmission capacity is determined by the tradeoff between the
incremental revenue from delivering additional electricity and the incremental cost of the
capacity increase. The optimization problems is solved numerically by using the search
algorithm to find the maximum point over the range of feasible transmission capacity;
0 1s≤ ≤ .
2.2 Two Wind Farms Model
The model with two wind farms assumes a branch line of “b” miles connecting farm 2
to farm 1, which is connected to the customer with a main line of “a” miles. If the two farms
are so distant that it is cheaper to connect each to the customer, the previous model applies.
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Load area
1st Farm
2nd FarmNetwork topology
A B
C
a miles
b miles
Figure 1: Simplified network topology of the model with 2 wind farms
This model explores the effect of output correlation on the optimal transmission
capacity. The basic one-farm model assumptions are retained and the two farms have the
same capacity. (K MW). The investor chooses the optimal size of both transmission lines
to maximize profit. The objective function is:
1 2
21 221 2 1 2 11 12 200 2, 0 1 1
( , , ) ( ) ( )(1 )
N
is s i
WC WCMAX NPV P q s s K aC s K bC s K WC WCr
β≤ ≤ ≤ ≤
=
+= − − − − −
+∑
s1 = the transmission capacity factor (main line)
s2 = the transmission capacity factor (branch line)
1( )aC s K = cost of a miles main transmission line capacity s1K MW built in year 0
2( )bC s K =cost of b miles branch transmission line capacity s2K MW built in year 0
11 12 and WC WC = cost of 1st and 2nd wind farms built in year 0
21 22 and WC WC = cost of 1st and 2nd wind farms built in year 20
1 2( , , )iq s s K = the expected delivered wind power at hour i from both wind farms
Note that 1 2 1 1 2 2( , , ) ( , ) ( , )i i iq s s K q s K q s K= + where 1 2 1( , , )iq s s K s K≤ . 1 1( , )iq s K is the
power generated by the 1st farm. 2 2( , )iq s K is the delivered power from the 2nd farm such
that 2 2 2( , )iq s K s K≤ .
Let 1 2 1 21
( , , ) ( , , )N
ii
q s s K Q s s K=
=∑ and 21 2211 12 20(1 )
WC WCWC WC WCr+
+ + =+
. The objective
function can be formulated as;
1 2 1 21, 2 ( , , ) ( ) ( )
s sMAX NPV PQ s s K aC s K bC s K WCβ= − − −
The optimization problem is solved numerically by evaluating the objective
function over a two-dimensional grid of s1 and s2 values.
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3. Data and variables
1. Wind data
We use hourly wind power generation data from four Northeastern U.S. wind
farms covering January-June and assume the July-December data are similar. The data
are shown in figure 1. The data were normalized so that the maximum output (the
nameplate capacity) was equal to 1. Descriptive statistics and output correlation &
distance between farms are shown in the tables below.
Figure 2: Hourly distribution of wind power
Wind farm Capacity factor (%) Variance
A 32.73 0.0840
B 34.73 0.0871
C 29.92 0.0821
D 29.77 0.0738
Table 1: Descriptive statistics of the wind farm output
Farm A
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 250 499 748 997 1246 1495 1744 1993 2242 2491 2740 2989 3238 3487 3736 3985 4234
Hours
% of nameplate capacity
Farm B
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 250 499 748 997 1246 1495 1744 1993 2242 2491 2740 2989 3238 3487 3736 3985 4234
Hours
% of name plate capacity
Farm C
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 223 445 667 889 1111 1333 1555 1777 1999 2221 2443 2665 2887 3109 3331 3553 3775 3997 4219
Hours
% of nameplate capacity
Farm D
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 223 445 667 889 1111 1333 1555 1777 1999 2221 2443 2665 2887 3109 3331 3553 3775 3997 4219
Hours
% of nameplate capacity
Farm A
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 250 499 748 997 1246 1495 1744 1993 2242 2491 2740 2989 3238 3487 3736 3985 4234
Hours
% of nameplate capacity
Farm B
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 250 499 748 997 1246 1495 1744 1993 2242 2491 2740 2989 3238 3487 3736 3985 4234
Hours
% of name plate capacity
Farm C
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 223 445 667 889 1111 1333 1555 1777 1999 2221 2443 2665 2887 3109 3331 3553 3775 3997 4219
Hours
% of nameplate capacity
Farm D
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 223 445 667 889 1111 1333 1555 1777 1999 2221 2443 2665 2887 3109 3331 3553 3775 3997 4219
Hours
% of nameplate capacity
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Farm A B C D
A 1.0 0.77 0.69 0.35
B 56 1.0 0.71 0.46
C 19 63 1.0 0.36
D 219 250 200 1.0
Note: correlations are shown on and above the diagonal and distances are shown below the diagonal.
Table 2: Output correlation and distance between farms (mile)
iq , ( , )Q s K , 1 2( , , )iq s s K and 1 2( , , )Q s s K are derived from this actual wind data.
2. Financial variable
The discount rate in this model is 10.4% (20% equity at 20% and 80% debt at 8%).
3. Transmission cost data and estimation
The cost of a transmission line varies with distance and terrain, but the greatest
uncertainty concerns regulatory delay and the cost of acquiring the land. To reflect this
uncertainty, we perform a sensitivity analysis with cost varying between 20% and 180%
of the base cost in the next section. We use DOE (2002) data to estimate the transmission
line cost function. The data are adjusted to reflect the current cost of DC transmission
construction1.1.
The functional form of the cost function is; cost per mile = e MWα β . The
coefficient β indicates how much cost increases as the line capacity increases by 1%;
elasticity with respect to line capacity. By using a log-log transformation, the
transmission line cost function is estimated as a log-linear function of transmission
capacity (MW). The transmission line cost, as a function of capacity is estimated using
ordinary least square (OLS); see Appendix A. As expected, the estimated result displays
economies of scale of transmission line investment.
cost per mile = 10.55415 0.5759e MW
1 The reported cost for high voltage transmission line covers a wide range (ISO-NE, 2007). If the cost of the transmission line were half or twice the cost we assume, the cost of the transmission would be halved or doubled assuming the capacity of the line is fixed.
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The regression equation has R2 = 0.94 and all parameters are statistically
significant. The t-statistics for the constant and the parameter of MW are 35.31 and 10.24
respectively.
4. Wind turbine cost
Costs of new wind turbines have risen and then fallen in the past few years; we
use $1,915/kW as the installed cost of a wind farm (Wiser and Bolinger, 2009),
$11.5/KW-year fixed O&M cost and $5.5/MWh variable O&M cost (Wind Deployment
System (WinDS) model (DOE, 2008b)).
5. Electricity price
The electricity price in this study is the real hourly electricity price paid to the owner
of the wind farm and transmission. Since the wind farm operator has little control over when
the turbines generate electricity, we assume that she receives the average price for the year
for each MWh. We assume that the delivered price paid to the wind farm investor is
$160/MWh included all federal and state subsidies. In addition, for simplicity, we assume the
electricity price over the next forty years is constant, after adjusting for inflation.
4. Results
4.1 Results for One Wind Farm
We focus on delivering wind power over a distance of 1,000 miles, about the
distance from Wyoming to Los Angeles; California’s renewable portfolio standard will
require large amounts of wind energy from distant sites. For a 1,000 mile long
transmission line, the optimal transmission capacity, utilization rate, profit and delivered
output for the four wind farms are shown in Appendix C, Table C1. The optimal capacity
is 74 - 79% of the wind farms’ capacity. As expected, among the four wind farms, those
with higher capacity factors have higher optimal transmission capacity, profit and
delivered output, with lower delivered power cost.
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
2
4
6
8
10
12 x 107
Transmission capacity factor (s)
Del
iver
ed o
utpu
t (M
Wh)
Farm A
0 100 200 300 400 500 6000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9Farm A: 1,000 miles
Price ($/MWh)
Tran
smis
sion
fact
or (s
)
Figure 3: Transmission capacity and delivered output
Figure 3 shows the relationship between the capacity of the transmission line and the
delivered wind power of Farm A. The slope of the curve represents the marginal benefit of
transmission capacity. As transmission capacity increases, marginal benefit decreases since
the turbine’s output is at full capacity for only a few hours per year. Farm A’s optimal
transmission capacity is 79% of the farm’s capacity, but the transmission line delivers 97% of
the wind power generated. Adding 21 percentage points to transmission capacity increases
delivered output by only 3 percentage points.
Figure 4: Price vs. transmission capacity factor (s)
Figure 4 shows the relationship between price and transmission capacity (s) of
farm A derived from the first order condition. The first order condition shows the optimal
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0 1 2 3 4 5 6 7 8 9 10 11x 107
40
60
80
100
120
140
160
Output (MWh)
Pric
e ($
/MW
h)
Farm A: 1,000 Miles
capacity decision, even when profit is negative, although the investor would not build the
wind farm and transmission for a negative return. At price below $55/MWh, the optimal
capacity is zero. Optimal transmission capacity and delivered power rise rapidly as price
goes from $55 to 200/MWh due to economies of scale in transmission investment and the
initial high marginal benefit of the transmission line (as seen in Figure 3). The scale
economies are essentially exhausted and virtually almost all of the generated power is being
delivered by the time a $300 price is reached; higher prices would increase transmission
capacity little.
As price rises, the value of the delivered electricity rises, increasing the value of
transmission capacity; almost all of the generated power is being delivered by the time a
$300 price is reached. The supply curve is shown in Figure 5.
The delivered cost of wind power (transmission cost included) ranges from $144
to 169/MWh for these 4 wind farms. Since the generation cost is $78 to 92/MWh,
transmission is 44-46% of the total cost; see Appendix C, Table C1. Note that the price
paid to the investor is $160/MWh.
Figure 5: The supply curve
The output distribution of a wind farm also affects the optimal transmission
capacity.2 In order to test the effect of the distribution, all 4 wind farms’ output data are
modified to have a 50%capacity factor. As shown in Appendix C Table C2, the optimal 2 Consider two wind farms with 30% capacity factor, if the turbine produced at 100% of capacity 30% of the time and zero capacity the rest, the optimal transmission capacity would be 100%; if it produced at 30% of capacity 100% of the time, the optimal transmission capacity would be 30%.
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transmission capacity, profit and delivered output of farms A, B and C are about the
same. However, Farm D has the lowest transmission capacity and the highest profit, since
it has less output distributed in the 80-100% of nameplate capacity range. As a result,
farm D faces less trade-off between transmission capacity and loss of high level output.
In addition, the farm with lower output standard deviation tends to have lower optimal
transmission capacity.
Transmission
capacity
factor (s)
Transmission
cost $
Additional
transmission
cost $
Additional
revenue $
Decrease in
profit $
A 0.7880 1.785 x 109 2.626 x 108 1.248 x 108 1.378 x 108
B 0.8075 1.810 x 109 2.373 x 108 0.946 x 108 1.427 x 108
C 0.7747 1.767 x 109 2.799 x 108 1.534 x 108 1.265 x 108
D 0.7388 1.720 x 109 3.276 x 108 1.049 x 108 2.227 x 108
Table 3: Implication of increasing transmission to 100% of wind farm capacity
Table 3 shows profit reduction in present value term when the transmission line is
expanded from the profit maximizing capacity to the wind farm’s nameplate capacity.
Profit reduction is calculated as the difference between the additional cost of building the
line at full capacity and revenue from additional delivered wind power (in present value);
expanding the line to full capacity costs $127 to $223 millions. Although it may seem
wasteful to spill some of the power generated by the wind farm, beyond the optimal
transmission capacity, the incremental cost of increasing transmission capacity is greater
than the value of the additional power delivered. For example, building a line at full
capacity for Farm A increases the cost of the line by 15% while delivering only 3% of
additional power.
The best wind sites are distant from load and so there is a tradeoff between lower
generation cost and lower transmission cost. Figure 6 shows the delivered cost of power
from wind farms with capacity factors of 35% and 50% as a function of the distance of
the wind farm from load. For a 50% capacity factor wind farm, the delivered cost of
power doubles when it is just over 1,063 miles away. For a 35% capacity wind farm, the
delivered cost of power is doubled when the wind farm is just under 1,000 miles away.
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0
50
100
150
200
250
0 200 400 600 800 1000 1200 1400 1600 1800Distance (mile)
$/MWh
35% Capacity Factor50% Capacity Factor
Figure 6: Cost and length of the transmission line of 2 wind farm sites
A more interesting interpretation of the figure is to see how much further you
would be willing to go to get power from a 50% capacity factor wind farm compared to a
35% capacity factor wind farm. At a cost of delivered power of $100/MWh, a 35%
capacity wind farm could be 300 miles away while a 50% capacity wind farm could be
1,000 miles away. Thus, if a 35% capacity factor wind farm were located 300 miles
away, the customer would be willing to go up to an additional 700 miles. For any
delivered cost of electricity, the horizontal difference between the two lines is the
additional distance a customer would be willing to go to get to a wind farm with capacity
factor 50% rather than 35%. Since much of the USA has a minimally acceptable wind
site within 300 miles, they would not find it attractive to go to the best continental wind
sites in the upper Midwest.
To ensure reliability, power systems must satisfy an N – 1 criterion. The
variability of wind output puts an additional burden on the generation system. The
cheapest way of meeting the N – 1 criterion is by using spinning reserve; this reserve can
also ramp up and down to fill the gaps in wind generation. As reported by CAISO (2008),
the total cost of ancillary services per MWh in 2008 (monthly average) is from $0.42-
1.92/MWh. This cost includes spinning reserve, non spinning reserve and regulation. The
cost of spinning reserve alone is about $0.15-0.67$/MWh. Thus, the cost of purchasing
spinning reserve would add less than 1% to the cost of delivered power.
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Farm A: 1,000 miles at price $160/MWh
60%
65%
70%
75%
80%
85%
90%
95%
100%
-80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80
Percentage change in tranmission cost
Tran
smis
sion
fact
or (s
)
80
100
120
140
160
180
200
220
Cos
t of d
eliv
ered
pow
er ($
/MW
h)
Transmission factor (s)Delivered power cost
Sensitivity analysis
We perform 4 sensitivity analyses: transmission cost vs. optimal capacity, the
optimal transmission capacity vs. length of the line, transmission capacity vs. the
discount rate, and profit vs. the discount rate. Other parameters are assumed to stay at
former levels.
Figure 7: Transmission cost and optimal line capacity of farm A
Transmission cost and optimal capacity
The optimal transmission capacity is solved for transmission cost varying plus or
minus 80% of the base line. When the transmission line costs 80% less than the base
case, the optimal size of the transmission line is 96% of the wind farm capacity and the
cost of delivered power is $96/MWh. When the transmission line costs 80% more than
the base case, the optimal capacity of the transmission line is 62% of the wind farm
capacity and the cost of delivered power is $210/MWh. The base case values have the
transmission line at 79% of the capacity of the wind farm with a delivered cost of
$149/MWh.
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0 200 400 600 800 1000 1200 1400 1600 1800 20000.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Tran
smis
sion
cap
actiy
fact
or (s
)
Farm A: price 160 $/MWh
Transmission length (mile)
0 5 10 15 20 25 30-2
0
2
4
6
8
10
12 x 109 Farm A: 1,000 miles, price 160 $/MWh
Discount rate (%)
Prof
it ($
)
Figure 8: Optimal transmission capacity and transmission length of farm A
Transmission capacity and length: Transmission cost increases with the length of the
line. Figure 7 can be interpreted as showing the effects of shortening the line to 200
miles or lengthening it to 1,800 miles. As transmission cost increases, the optimal
capacity of the transmission line relative to the wind farm capacity decreases for a given
power price, as shown in Figure 8. A longer transmission line results in lower delivered
output.
Figure 9: Profit and discount rate of farm A
19
0 10 20 30 40 50 60 700
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Discount rate (%)
Tran
smis
sion
cap
acity
fact
or (s
)Farm A: 1,000 miles, price 160 $/MWh
Profit and a discount rate: Profit steadily decreases as the discount rate increases. As
shown in Figure 9, the IRR (Internal Rate of Return) of this project is around 14% at a
$160/MWh price (the discount rate giving zero NPV).
Figure 10: Optimal transmission capacity and discount rate of farm A
Transmission capacity and discount rate: Increasing the cost of capital (equity and loans)
increases the cost of the transmission line. Figure 10 shows that the capacity of the line
declines as the discount rate increases.
4.2 Results for Two Wind Farms
The data from 4 wind farms is used to maximize profit when two wind farms
share the same central transmission line. By bundling 2 wind farms, the capacity of the
main transmission line is almost double compared with the one wind farm case and so the
transmission line can take advantage of economies of scale at this level (see Appendix C
Table C3 for detail). The correlation between outputs of wind farms generally decreases
as the farms are more distant. Here we investigate connecting wind farms that are more
distant, trading off the cost of the additional transmission against the lower correlation of
output. We examine each of the 12 possible pairs. Note that the pair AB means that the
main transmission line goes to A, with a secondary line to B. The results from AB and
BA are similar. The model is solved under 3 scenarios.
− Scenario 1: a = 1,000 miles and b = the actual distance between farms
20
− Scenario 2: a = 1,000 miles and b = the distance calculated from the estimated
relationship between correlation and distance (Appendix B). Farm A is paired
with a fictitious wind farm whose capacity factor is the same as A where the
correlation between the outputs of the two wind farms is calculated from the
estimated correlation-distance relationship.
− Scenario 3: This scenario has the same configuration as scenario 2 but
imposes a penalty per MWh when the delivered power from the wind farms
falls below a minimum requirement level.
In scenario 1, the total cost of wind power (both generation and transmission cost
included) ranges from $134 to 153/MWh, taking advantage of the economies of scale in
transmission. The cost of generation ranges from $80 to 92/MWh, approximately the
same as the one wind farm model. Transmission cost still accounts for more than one
third of the delivered wind power cost.
When the second wind farm is close to the first, the output from the two wind
farms are highly correlated. The second wind farm would help lower the delivered cost of
electricity through economies of scale of transmission but this cost saving must be traded
off against the length of the connecting transmission line.
In addition, when the length of the second transmission line is shorter, the
capacity of the line (s2) is higher. A shorter line translates to lower cost, which makes a
slightly higher capacity more profitable. In addition, like the one wind farm model,
capacity factor is the key factor that determines profit from the project.
Given the correlation-distance relationship, in scenario 2, we vary the correlation
over the relevant range, calculate the implied distance, and then optimize the capacity of
the transmission line to maximize profit. Farm A is paired with a wind farm of the same
capacity, but we vary the distance (and thus the output correlation) between the two
farms. The simulated data used in scenario 2 are random numbers generated with the
specific correlation with farm A and have capacity factor 30%.
While the correlation of output from two wind farms decreases with the distance
between them, the correlation also varies with terrain and wind direction. The pair of
wind farms with lower correlation tends to have higher utilization rate of the main
transmission line. This can be considered as the effect of output smoothing by
21
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8Correlation
Profit ($billion)
aggregating wind farms with low output correlation. The transmission line is used more
efficiently when output is smoother (see Appendix C Table C4 for detail). If the system
needs the smoother wind power output, more money is needed to invest in longer
transmission.
Lower output correlation implies lower transmission capacity and higher
transmission (main line) utilization rate. Without a price premium for smoothed output,
the shorter distance between farms is more profitable than a low correlation. Thus, for
this distance-correlation relationship, investors would want to build wind farms close
together, despite the high correlation of their outputs. Thus, the optimal distance between
wind farms is zero, as long as the second farm has the same capacity factor as the first.
Figure 11: Profit at penalty $160/MWh with minimum delivery requirement 400 MW
Scenario 3 analyzes the effect of imposing a minimum output requirement of 400
MW (20% of the total nameplate capacity) by the buyer. If the wind farm cannot fulfill
this requirement, it has to buy power from other generators or pay the buyer the financial
penalty. This cost is defined as an imbalance price. In addition, this imbalance price is
assumed to be higher than or equal to the price paid to the wind farm.
As expected, the pair with lower correlation has lower imbalance output. As
shown in Appendix C Table C5, the imbalance output (the amount in MWh that cannot
meet the requirement) increases steadily as the correlation between wind farms’ output
increases. In addition, the result from this scenario shows the different investment
decision from scenario 2. In scenario 2 without the minimum output requirement penalty,
the wind farm projects with high output correlation and short transmission line are more
22
profitable. Imposing the minimum requirement increases the optimal distance between
wind farms, resulting in an optimal output correlation in the range 0.4 – 0.6, as shown in
Figure 11.
5. Conclusion
This analysis illustrates the complications with deciding where to site wind farms,
trading off the lower cost of better wind potential against transmission cost, how large a
transmission line to build, and where to locate a second wind farm if it is to be connected
to the load with the same transmission line. The results are based on actual data with
some extensions. The wind farm capacity factors, costs of transmission, and correlation
among wind farms are unique to each location; an analysis of a specific location could be
optimized using the methods presented here.
Since a 1,000 mile transmission line roughly doubles the delivered cost of power,
decreasing the variability of generation at the wind farm lowers power costs. However,
two connected wind farms only raise the capacity factor slightly. Imposing a minimum
requirement penalty leads to changes that increase firm output, although raising the
generation cost.
For a wind farm with a 1,000 mile transmission line, about the distance from
Wyoming to Southern California, the intermittency and low capacity factor of wind farms
increases the cost of transmission significantly. We find that the delivered cost of power
and optimal capacity of the transmission line increase with the price paid for the power,
and decrease with the wind farm’s capacity factor, the distance from load, and the
discount rate.
For a delivered price of $160/MWh, the optimal capacity of the transmission line
is 74-79%; only 3% of generated power is wasted for this transmission line. When two
wind farms are bundled, economies of scale in transmission increase the optimal capacity
of the transmission line and lower the cost of delivered power. When we examine the
distance between wind farms, trading off lower output correlation with greater distance
between farms, we find that closer farms have the lowest cost of delivered power.
23
However, when there is a penalty for failing to deliver a minimum amount of power, the
distant wind farms become more profitable.
24
3 3.5 4 4.5 5 5.5 6 6.5 712.5
13
13.5
14
14.5
15
log(MW)
log(
cost
)
log(cost) = 10.5541 + 0.5759log(MW)
Appendix A: Transmission cost function estimation
The data used for transmission cost function estimation are from DOE (2002) which
is the cost data from 1995 study. The data are adjusted by the factor of 3. We need to adjust
the data that makes the approximation close to the current cost range of transmission line.
The factor of 3 gives the estimated transmission within the range of the observed
transmission project cost. The transmission cost data is the limitation in this model. The cost
data at different thermal capacity from the same source is necessary for estimating the cost
function. In the future, when more appropriate cost data is available, the approach here can be
applied. In addition, the actual cost of the DC line, if available, is an alternative for the study.
ln(cost) = 10.55415+ 0.5759*ln(MW)
Variable Coefficient Std. Error t-Statistic Prob.
constant 10.55415 0.298873 35.31313 0.0000
ln(MW) 0.575873 0.056237 10.24006 0.0000
R-squared 0.937421 F-statistic 104.8589
Adjusted R-squared 0.928481 Prob(F-statistic) 0.000018
S.E. of regression 0.194477 Log likelihood 3.097459
Sum squared resid 0.264748 Durbin-Watson stat 1.814451
Table 1: Transmission cost function estimation result
Figure 1: Estimated transmission cost vs. actual cost (log-linear)
25
Appendix B: Relationship between distance and wind-output correlation
We use the wind speed data from 9 wind speed observation sites in Colorado
(UWIG, 2007) to estimate the relationship between distance and correlation. There are
3,909 hourly wind speed observations used for correlation coefficient estimation.
According to Manwell et al (2002), wind power (P) per area (A) is the function of the
wind speed (V) and air density (ρ).
312
P VA
ρ=
Note that we used the same data source as DOE (2005) but we set some wind
speed observations that are lower than the cut-in speed or higher than the cut-out speed to
be 0. The cut-in speed and the cut-out speed 3 of the wind turbine is 4.5 m/s and 30 m/s
respectively (Gipe, 2004). We calculate the correlations coefficients of the cubic wind
speed (V3) among the wind speed observation sites. Given that other variables in the
formula (A and ρ) held constant, the correlation coefficients calculated V3 are the
estimated correlation coefficients of wind power among the wind sites.
Various models of distance and correlation are estimated including linear,
quadratic and linear-log (correlation is a function of ln(distance)). Ordinary Least Square
(OLS) is used for the estimation. The linear-log model used by DOE (2005) is more
suitable than the linear and quadratic models.
Note that in Figure B1 (right) some observations are deviate far from the
estimated line, for example, close wind stations with low correlation. This could be due
to terrain such as a ridge between the nearby locations.
3 From Gipe (2004), cut-in wind speed is the wind speed that a wind turbine starts to generate power. The wind turbine cannot generate power if the wind speed is lower than the cut-in level. Cut-out wind speed is the wind speed at which the wind turbine stops generating electricity in order to protect the equipment from an excessive wind speed. The wind turbine cannot generate power if the wind speed is higher than the cut-out level.
26
Distance (mile)
Correlation
0 100 200 300 400 500 6000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Distance (mile)
Correlation
0 100 200 300 400 500 6000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
data linear quadratic
Figure B1: Linear and quadratic models (left) and linear-log model (right)
The linear-log model, correlation = a + b*ln(distance), seems best for this study.
The shape of the curve is similar to the curve from NREL (2007).
Correlation = 1.557018 – 0.231544*ln(distance)
Table B1: Correlation and distance estimation result
Variable Coefficient Std. Error t-Statistic Prob.
constant 1.557018 0.145054 10.73408 0.0000
ln(distance) -0.231544 0.029868 -7.752362 0.0000
R-squared 0.638679 F-statistic 60.09911
Adjusted R-squared 0.628052 Prob(F-statistic) 0.000000
S.E. of regression 0.123475 Durbin-Watson stat 1.446861
Sum squared residual 0.518366 Log likelihood 25.24887
27
Appendix C: Computation results
Farm Capacity
factor
Trans.
factor (s)
Trans.
utilization Profit
Cost
$/MWh
$/MWh
(turbine)
Delivery
(MWh)
Delivery/
Generation
A 32.73 % 0.7880 40.22% 1.75 x 108 153.31 82.24 1.11 x 108 97.10%
B 34.73 % 0.8075 42.00% 4.43 x 108 144.20 77.78 1.19 x 108 97.93%
C 29.92 % 0.7747 37.02% -2.05 x 108 168.68 91.99 1.01 x 108 96.11%
D 29.77 % 0.7388 39.11% -1.28 x 108 165.35 91.31 1.01 x 108 97.32%
Table C1: 1,000 mile transmission line at price $160/MWh
Farm Standard
deviation
Trans.
factor (s)
Trans.
utilization Profit
Cost
$/MWh
$/MWh
(turbine)
Delivery
(MWh)
Delivery/
Generation
A 0.2472 0.9135 54.39% 3.39 x 108 77.45 53.10 1.74 x 108 99.64%
B 0.2594 0.9117 54.56% 3.40 x 108 77.33 53.04 1.74 x 108 99.77%
C 0.2337 0.9212 53.95% 3.39 x 108 77.55 53.09 1.74 x 108 99.66%
D 0.2231 0.8817 56.44% 3.42 x 108 76.84 53.02 1.74 x 108 99.79%
Table C2: 1,000 mile transmission line with 50% adjusted capacity factor farm at price
$160/MWh
28
Table C3: 1,000 mile main transmission line and actual distance between farms at price
$160/MWh
Pair Corr.
(mile)
Trans (s1)
utilization,%
Trans
(s2) Profit
Cost
$/MWh
Cost $/MWh
(turbine)
Delivery
(MWh)
Delivery/
Generation
AB 1.6330
(40.61) 0.8952 1.50 x 109 132.69 79.57 2.32 x 108 98.78 %
BA
0.7665
(56) 1.6326
(40.61) 0.8988 1.50 x 109 132.71 79.58 2.32 x 108 98.85 %
AC 1.5586
(39.22) 0.9864 0.95 x 109 141.08 86.33 2.14 x 108 97.83 %
CA
0.6919
(19) 1.5587
(41.32) 0.9925 0.95 x 109 141.09 86.33 2.14 x 108 97.83 %
AD 1.4013
(43.32) 0.8124 0.69 x 109 146.18 86.93 2.13 x 108 97.74 %
DA
0.3471
(219) 1.3984
(43.32) 0.8829 0.69 x 109 146.65 87.01 2.13 x 108 97.71 %
BC 1.5641
(40.36) 0.9382 1.12 x 109 138.40 83.59 2.11 x 108 98.05 %
CB
0.7074
(63) 1.5678
(40.29) 0.9196 1.13 x 109 138.37 83.55 2.21 x 108 98.06 %
BD 1.4073
(44.50) 0.7929 0.89 x 109 142.79 84.25 2.19 x 108 97.88 %
DB
0.3552
(250) 1.4141
(44.33) 0.8649 0.87 x 109 143.27 84.18 2.20 x 108 97.87 %
CD 1.4159
(40.80) 0.8038 0.33 x 109 153.12 91.34 2.02 x 108 97.49 %
DC
0.4572
(200)
1.3981
(41.21) 0.8980 0.30 x 109 153.66 91.59 2.02 x 108 97.21 %
29
Pair Corr.
(mile)
Trans (s1)
utilization, %
Trans
(s2) Profit
Cost
$/MWh
Cost $/MWh
(turbine)
Delivery
(MWh)
Delivery/
Generation
A,
A30
0.30
(227)
1.1865
(51.70) 0.5799 1.07 x 109 138.81 86.03 2.15 x 108 98.28 %
A,
A35
0.35
(184)
1.1948
(51.13) 0.5769 1.10 x 109 138.25 86.38 2.14 x 108 98.26 %
A,
A40
0.40
(147)
1.2105
(50.64) 0.5771 1.16 x 109 137.07 86.07 2.15 x 108 98.36 %
A,
A45
0.45
(119)
1.2180
(50.34) 0.5980 1.20 x 109 136.37 86.07 2.15 x 108 98.32 %
A,
A50
0.50
(96)
1.2493
(49.53) 0.6459 1.27 x 109 135.23 85.27 2.17 x 108 98.28 %
A,
A55
0.55
(77)
1.2503
(49.13) 0.6186 1.25 x 109 135.57 85.90 2.15 x 108 98.43 %
A,
A60
0.60
(62)
1.2585
(48.75) 0.6224 1.24 x 109 135.45 86.00 2.15 x 108 98.35 %
A,
A65
0.65
(50)
1.2716
(48.22) 0.6382 124 x 109 135.47 86.06 2.15 x 108 98.30 %
A,
A70
0.70
(40)
1.2952
(47.49) 0.6323 1.26 x 109 135.21 85.78 2.16 x 108 98.44 %
A,
A75
0.75
(33)
1.3240
(48.04) 0.6689 1.23 x 109 135.82 85.89 2.15 x 108 98.49 %
A,
A80
0.80
(26)
1.3314
(46.07) 0.6769 1.22 x 109 135.95 86.03 2.15 x 108 98.32 %
Table C4: Farm A paired with farms at different correlation (capacity factor 30%) with
1,000 mile main transmission line and the distance between farms calculated from
relationship in Appendix B at price = $160/MWh
30
Pair Corr.
(mile)
Profit @
penalty
$160/MWh
Profit @
penalty
$180/MWh
Profit @
penalty
$200/MWh
Imbalance
(MWh)
Delivery
(MWh)
Imbalance
/ Delivery
(%)
A,
A30
0.30
(227) 4.71 x 108 3.95 x 108 3.20 x 108 1.60 x 107 2.15 x 108 7.44%
A,
A35
0.35
(184) 4.84 x 108 4.08 x 108 3.31 x 108 1.63 x 107 2.14 x 108 7.61%
A,
A40
0.40
(147) 5.28 x 108 4.49 x 108 3.70 x 108 1.68 x 107 2.15 x 108 7.81%
A,
A45
0.45
(119) 5.44 x 108 4.62 x 108 3.81 x 108 1.73 x 107 2.15 x 108 8.06%
A,
A50
0.50
(96) 5.89 x 108 5.05 x 108 4.20 x 108 1.79 x 107 2.17 x 108 8.28%
A,
A55
0.55
(77) 5.39 x 108 4.52 x 108 3.64 x 108 1.86 x 107 2.15 x 108 8.63%
A,
A60
0.60
(62) 4.97 x 108 4.04 x 108 3.10 x 108 1.98 x 107 2.15 x 108 9.21%
A,
A65
0.65
(50) 4.58 x 108 3.60 x 108 2.62 x 108 2.08 x 107 2.15 x 108 9.68%
A,
A70
0.70
(40) 4.35 x 108 3.52 x 108 2.51 x 108 2.14 x 107 2.16 x 108 9.92%
A,
A75
0.75
(33) 3.50 x 108 2.40 x 108 1.30 x 108 2.33 x 107 2.15 x 108 10.81%
A,
A80
0.80
(26) 3.09 x 108 1.96 x 108 0.83 x 108 2.41 x 107 2.15 x 108 11.20%
Table C5: Farm A paired with farms at different correlation (capacity factor 30%) with
1,000 mile main transmission line and the distance between farms calculated from
relationship in Appendix B at price = $160/MWh with 400 MW delivery requirement
31
Reference
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w_sale.html (accessed July 13, 2007).
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Modeling System, Department of Energy, June 2005.
DOE (2007), Wind Energy Resource Potential, Office of Energy Efficiency and Renewable
Energy, Department of Energy. Document available online at:
http://www1.eere.energy.gov/windandhydro /wind_potential.html (accessed July 9, 2007).
DOE (2008a), Annual Report on U.S. Wind Power Installation, Cost, and Performance
Trends: 2007, Office of Energy Efficiency and Renewable Energy, Department of
Energy (DOE), May 2008.
DOE (2008b), 20% Wind Energy by 2030: Increasing Wind Energy’s Contribution to
U.S. Electricity Supply, Office of Energy Efficiency and Renewable Energy,
Department of Energy (DOE), July 2008.
Denholm P. and Sioshansi R. (2009) The value of compressed air energy storage with
wind in transmission-constrained electric power systems. Energy Policy 37(8),
3149-3158
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Gipe P. (2004), Wind Power: Renewable Energy for Home, Farm and Business. Chelsea
Green Publishing Company, VT.
ISO-NE (2007), Scenario Analysis-Transmission & Distribution Conceptual Cost, ISO
New England. Document available online at: http://www.iso-
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(accessed January 16, 2009).
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33
Chapter 2 The optimal baseload generation portfolio under CO2 regulation and
fuel price uncertainties
Introduction
NERC (North American Electric Reliability Corporation) predicts that many
regions in the US will need significant investment in electricity generation in the near
future (NERC, 2009). Electricity suppliers face difficult decision concerning which
technology to invest. New generation plants are capital intensive and have a long lead
time. Once a plant is built, capital becomes sunk and the plant/technology will be locked
in for 20-60 years. Uncertainty about environmental regulation and variability in fuel
price during the plant’s lifetime make the decision difficult.
According to Awerbuch (2003), traditional power system planning attempts to
minimize cost of power generation while risk factors are not taken into account explicitly.
In the next few decades, the power sector will face many challenges especially the tighter
environmental regulation on green house gas emission. Future cost of CO2 regulation is
uncertain.
While choosing the best technology for each plant is important, choosing a
portfolio of technologies/fuels is more important in managing risks in an uncertain world.
A natural gas combined cycle (NGCC) generator may have the lowest expected cost but
the observed past volatility in gas price suggests that a portfolio of 100% NGCC is likely
to have higher variability than a portfolio of different technologies. An optimal portfolio
can have the dominated technology if it has negative correlation with other technologies
leading to lower variance portfolio.
34
The expected cost and cost variability of the generation assets portfolio depend on
the mix of generation technologies in the portfolio. Each generation asset (technology)
has a different risk and cost profile. Even if a single fuel-technology choice had lower
cost and variability than all others, the variability of the portfolio would be greater than
one with a mix of technologies/fuels (a more conventional way of stating this that it
would be imprudent to have only one type of asset in the system). Thus, the planner has
to choose the mix of fuel-technology plants that optimizes cost and risk of the generation
asset.
The mean-variance portfolio model is a tool that can formulate the efficient trade-
off between risk and return. This model has been widely used in the finance field. This
study applies the mean-variance portfolio theory to a model that optimizes the technology
portfolio for the power system. In this study, we derive the optimal portfolio frontier by
focusing mainly on the variability in the fuel markets and the range of prices that could
be imposed on CO2 emissions. Whether the regulation is in the form of a carbon tax or a
cap and trade system, there will be a market clearing price for a ton of CO2 emissions.
We refer to this as the CO2 prices. The model constructs optimal portfolios assuming
scenarios with a range of CO2 price, fuel prices, capital cost and the cost of carbon
capture and storage (CCS). In addition, the study uses the mean variance portfolio model
with a Bayesian technique that allows decision makers to input their beliefs about the
likelihood of each scenario.
Literature review
The mean-variance portfolio model was developed by Markowitz (1952). The
model assumes the mean and variance of the portfolio are the two factors that matter to
the investor. The investor is assumed to love ‘return’ and avoid ‘risk’ (variance).
Investor’s utility is a function of wealth derived in term of return (r) from investment. By
assuming a normal distribution of asset return and using a Taylor’s series expansion, the
expected utility function can be derived as the function of mean return and variance
(Huang and Litzenberger, 1988).
35
21[ ( )] ( [ ]) ''( [ ])2 rE U r U E r U E r σ= +
The expected utility function is an increasing function of mean (return) and
decreasing function of risk (variance); the utility function is concave where '( ) 0U ⋅ ≥ and
''( ) 0U ⋅ ≤ . Thus, in order to maximize the expected utility, the investor chooses the
portfolio that yields the highest return at the given variance (standard deviation) or the
portfolio with the lowest variance at the given return.
The optimization of the mean-variance portfolio model is shown below. The
investor chooses the portfolio weight of each asset that minimizes the portfolio variance
given the specific value of portfolio return.
Min 1 1
12
N N
i j iji j
w w σ= =∑∑
Subject to: 1
1N
ii
w=
=∑ and 1
N
i ii
w r μ=
=∑
iw is the portfolio weight of asset i (N assets in total). ijσ is the covariance of asset
i and j . ir is the return of asset i. μ is the target return of the portfolio (constant). The
optimization problem can also be written in the matrix form.
w
1Min 2
Σw' w
Subject to: 1w'1 = and R μ=w'
Σ is the covariance matrix of asset return where the diagonal elements represent
variance of the asset and the off-diagonal terms represent covariance between assets. w
is the Nx1 vector of portfolio weight. R is the Nx1 vector of asset return. 1 is Nx1 vector
of one.
The model is made operational by assuming the return and variance can be
estimated from recent market data. In effect, this narrows the theory and it is operational
as short term within the model. The mean-variance portfolio model uses the historical
movement in asset return to formulate the optimal portfolio. This approach may not
support the investor’s belief about the future return. Black and Litterman (1991) and
(1992) (thereafter “BL”) apply the Bayesian statistical theory to the conventional mean-
36
variance portfolio model. This model enables an investor to express his belief on the
future asset return.
In order to accommodate the individual’s view in portfolio formulation, BL use
the market equilibrium portfolio as the neutral starting point. The individual can express
his subjective view or belief on the asset return which can be different from the
equilibrium return. (BL use the term “view” to represent the posterior belief on the
asset’s return). Using Bayesian statistical theory, we can estimate the posterior asset
return and covariance matrix given the individual belief using the following formulation.
Posterior return: -1-1 -1 -1 -1' 'blR P P P Q⎡ ⎤ ⎡ ⎤= Σ + Ω Σ Π + Ω⎣ ⎦ ⎣ ⎦
Covariance matrix: 1 1 1( ' )bl P P− − −Σ = Σ + Σ + Ω
Σ is the covariance matrix of prior asset return (NxN matrix), P is the matrix
(KxN) represented the assets in the posterior belief, K is the number of assets expressed
in the posterior belief, Ω is the covariance of posterior belief (KxK matrix),Π is the
equilibrium return (Nx1 vector) and Q is the posterior belief vector (Kx1). The proof of
the above formulation is presented in Satchell and Scrowcroft (2000).
The confidence level of the individual’s belief is represented by the covariance
matrix of belief (Ω ) where 1( 1)P Pc
Ω = − Σ (Meucci, 2005). (0,1]c∈ indicates the level of
confidence; c close to 0 means low confidence and c close to 1 means high confidence.
High variance indicates low confidence in belief. Note that the variance of return is the
sum of prior variance and variance of the posterior belief.
Many studies have attempted to apply the mean-variance portfolio theory to the
energy and electric utility sector. Bar-Lev and Katz (1976) did the pioneer study applying
the model to find the optimal fossil fuel mix for a power utility. “Return” of the fossil
fuel is defined as Btu4/$; the inverse of the fuel cost. The standard deviation is calculated
from the inverse of the fuel cost data. However, the model is incorrectly defined such that
return and weight do not match according to the theory5.
4 Btu or British thermal unit is the unit of energy used for measuring the heat content. 5 From the mean-variance portfolio theory, return = payoff of asset ($)
money invested in asset ($)i
iand weight
= money invested in asset ($)total investment ($)
i . The denominator (cost of asset i) from ‘return’ and denominator (money
37
Other studies repeating Bar-Lev and Katz (1976)’s mistake include Humphreys
and McClain (1998) for U.S. fossil fuel portfolio, Awerbuch and Berger (2003) and
Awerbuch (2006) for power generation technology portfolio.
Alternatively, Doherty et al. (2005) uses the risk-cost framework instead of risk-
return to solve for the efficient generation portfolio for Ireland in 2020. Under the risk-
cost framework, the definition of cost and weight are consistent. However, they do not
explain the theoretical framework under the mean-variance portfolio theory.
Roques et al. (2006) applies the mean-variance portfolio theory to solve the
optimal technology portfolio for the private investors incorporating electricity, fuel and
CO2 price risks. Historical prices of electricity, fuel and CO2 in UK are used for the
study. Return is defined as the net present value (NPV) per GW of generation capacity.
NPV is calculated from electricity sale revenue (using spot electricity price) and
generation cost. The simulated CO2 tax with the average of £40/ton and standard
deviation of 10 is included in power generation cost.
Our study uses the risk-cost framework to analyze the power generation
technology portfolio. Our definition of cost is the cost of electricity generation per MWh.
This study aims to find the efficient risk-cost portfolio such that the portfolio has the
lowest variance (standard deviation) at the given level of cost.
This study goes further in reinterpreting the mean-variance portfolio theory for an
electricity investment decision. We calculate power generation cost (levelized cost of
electricity) using the cost components such as capital cost, economic lifetime, capacity
factor, discount rate, historical fuel price, operation and maintenance costs and CO2 price.
This approach gives flexibility in power generation cost calculation and scenario
formulation.
The contribution of this study includes the analysis of the optimal portfolio under
different scenarios on generation cost components such as fuel cost and CO2 price. The
analysis on capital cost of the plant is also included in the study. The possible range of
capital cost is tested in order to examine the effect on the optimal portfolio. Our study invested in asset i) from ‘weight’ match each other. If return on fuel is defined as Btu
money paid for fuel ($)i,
the correct weight must be money paid for fuel ($)total payment on all fuel ($)
i because Btu is the payoff from investing in fuel i.
38
explains the theoretical formulation of the risk-cost framework under the mean-variance
portfolio theory which is not presented in the previous studies. In addition, we show an
example applying the Bayesian analysis to formulate the optimal power generation
portfolio given the investor’s belief on cost.
Model
The first step is to solve for the efficient power generation technology-fuel
frontier. Having defined the efficient frontier, the planner must decide which
combination of risk/cost is preferred. Rather than suggest an optimal risk/cost ratio, we
finesse this choice and show the optimal portfolio for all risk/cost ratios on the efficiency
frontier. The optimal portfolio depends on the planner’s preference regarding to the
tradeoff between cost and variation in cost.
The model here is focused on the baseload6 generation that produces 75-85% of
power during a year. It accounts for the majority of investment and utilities’ expenditure.
Power generation portfolio
The model for analyzing the optimal power generation portfolio is modified from
the conventional mean-variance portfolio model where the individual maximizes his
utility (wealth) by selecting the portfolio that has the lowest variance given the return.
For the application to the power generation portfolio, the convention model is adjusted
such that the optimal portfolio has the lowest variance given the expected cost of the
portfolio. Another important difference is that the low transactions cost of financial
markets means that the individual can rearrange her portfolio to the optimal one.
Electricity generators are illiquid and there are high transactions costs for rearranging the
generation mix.
The utility function is concave and strictly increasing in wealth. The expected
utility function is a decreasing function of both cost and variance. Let V be the value or 6 According to Energy Information Administration (EIA), the baseload (demand) is “the minimum amount of electric power delivered or required over a given period of time at a steady rate” (EIA, http://www.eia.doe.gov/glossary/glossary_b.htm).
39
benefit from electricity which is assumed to be constant and independent of electricity
cost (C). Thus, the utility function from electricity consumption is a function of the net
value; U( - )V C . Applying Taylor’s series approximation around -E[ ]V C , we can derive
the expected utility function which is a decreasing function in both cost and variance.
23
1( ) ( [ ]) '( [ ])( [ ]) ''( [ ])(( [ ])2
U V C U V E C U V E C V C V E C U V E C V C V E C R− = − + − − − + + − − − + +
23
1 ( - [ ]) '( - [ ])( [ ] - ) ''( - [ ])( [ ] - )2
U V E C U V E C E C C U V E C E C C R= + + +
23
1[ ( )] ( [ ]) '( [ ]) [( [ ] - )] ''( [ ]) [( [ ] ) ] [ ]2
E U V C U V E C U V E C E E C C U V E C E E C C E R− = − + − + − − +
21 ( [ ]) ''( - [ ])2 CU V E C U V E C σ= − +
21( - [ ]) -2 CU V E C βσ=
3R is the higher degree terms from Taylor’s approximation and 3[ ] 0E R = from
the normal distribution assumption. ''( - [ ]) 0U V E C < (from concavity); β is the positive
constant. Since the utility function is a decreasing function in cost (C), the expected
utility function is decreasing in the expected cost (E[C]) and variance of cost ( 2Cσ ). Thus,
the planner chooses the optimal portfolio which has the lowest variance given the cost of
the portfolio. Note that there is no theoretical derivation of the expected utility function
using cost and variance in the previous studies which use the risk-cost framework.
Baseload generation technology portfolio
The optimization approach for the baseload generation portfolio is similar to the
conventional mean-variance portfolio. Additional constraints require that the weight of
each technology is greater than zero.
Min 1 1
12
N N
i j iji j
w w σ= =∑∑
Subject to: 1
1N
ii
w=
=∑
1
N
i ii
w c μ=
=∑
0iw ≥ for all i
40
There are N baseload technologies with the respective cost (ci) and weight (wi) for
i = 1-N. ijσ is the covariance between generation cost of technology i and j. μ is the
positive constant representing the given cost level.
All portfolios considered are assumed to satisfy baseload electricity demand. In
other words, all portfolios generate the same amount of electricity. Given that all
portfolios yield the same output, the optimal portfolio is the one that has the efficient
tradeoff between cost and variance.
The Bayesian analysis or BL model can be applied to the baseload generation
portfolio model directly. The generation cost calculated from the baseline model is used
as the neutral starting point (BL model uses an equilibrium return as the starting point).
An individual can express a belief on power generation cost of one or more baseload
technologies. The belief can be expressed as an absolute belief (i.e. return of asset A is
expected to be at 14%) or the relative belief (i.e. return of asset A is expected to be higher
than asset B by 2%).
The baseload generation portfolio in this study includes 7 technologies. The
current technologies which already operate commercially include nuclear, PC (pulverized
coal), NGCC (Natural Gas Combined Cycle). The prospective future technologies
include IGCC (Integrated Gasification Combined Cycle), IGCC with CCS (Carbon
Capture and Storage), PC with CCS and NGCC with CCS. The detail on power
generation cost data and assumption on the cost is presented in the appendix.
Results
The mean-variance portfolio model for baseload power generation technology
evaluates technologies with different characteristics. Nuclear has high capital cost and
relatively low fuel costs, giving it low variance. PC, IGCC, IGCC CCS and PC CCS are
technologies with somewhat lower capital cost. NGCC and NGCC CCS are the
technologies with relatively low capital cost and high variable cost; mainly fuel cost.
Nuclear emits zero CO2 in the generation process. PC and IGCC are technologies
with high CO2 emission per MWh. NGCC emits around half of CO2 per MWh compared
41
with PC. IGCC and NGCC with CCS capture most of the CO2 in the power generation
process. In this section, we formulate the optimal mean-variance portfolio under various
scenarios of CO2 price, fuel price structure, capital cost and CCS cost.
1. The baseline model
The baseline model uses the fuel price data from 1990-2009. The optimal
portfolios are formulated under 2 scenarios of CO2 prices; $20 and 40/ton of CO2. The
first 2 models (B1 and B2) include 3 current baseload technologies; nuclear, PC
(pulverized coal) and NGCC (Natural Gas Combined Cycle). Models B3 and B4 include
these 3 current technologies and prospective future technologies including IGCC
(Integrated Gasification Combined Cycle) and PC, NGCC and IGCC with CCS (Carbon
Capture and Storage).
• B1: Portfolio of 3 current technologies under $20/ton CO2 price
Table 1: Cost/standard deviation (left) and the correlation matrix (right)
Figure 1: The efficient frontier (left) and technology mix along the frontier (right)
The left hand side of figure 1 shows the efficient frontier. The right hand side
shows the composition of the optimal portfolio for each cost-standard deviation. For
Cost/MWh S.D. Nuclear PC NGCC
Nuclear 106.75 2.20 Nuclear 1.00 0.11 -0.02 PC 73.42 5.53 PC 0.11 1.00 0.05 NGCC 59.82 14.03 NGCC -0.02 0.05 1.00
Nuclear
PC
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
59.9 63.3 66.7 70.1 73.5 76.9 80.3 83.7 87.1 90.5 93.9 97.3 100.7
14.0 10.9 8.1 5.9 5.1 4.7 4.2 3.8 3.4 3.1 2.7 2.4 2.2 2.1
2 4 6 8 10 12 1450
60
70
80
90
100
110
Cost ($/MWh)
S.D.
NGCC
PC
Nuclear
S.D.
Cost ($/MWh)
42
example a standard deviation of 6 corresponds to a cost of $68/MWh. The optimal
portfolio consists of 65% PC and 35% NGCC while the efficient frontier on the left hand
sides shows cost-standard deviation; it does not identify the composition of the portfolio.
In the first scenario, the CO2 regulation cost is set at $20/ton with standard
deviation of 5. NGCC is the lowest cost technology but has the highest standard
deviation. The opposite is true for nuclear. Thus, the lowest cost portfolio is 100% NGCC
having high standard deviation at 14. Minimizing the standard deviation leads to a
portfolio dominated by nuclear with some PC and a tiny share of NGCC. Low correlation
between NGCC and nuclear leads to a small share of NGCC that lowers the variance of a
portfolio when the share of nuclear increases. PC and nuclear dominate portfolios on the
efficient portfolio as the standard deviation decreases. At a portfolio cost around
80/MWh with standard deviation 4, the portfolio consists of 25% nuclear, 55% PC and
20% NGCC.
• B2: Portfolio of 3 current technologies under $40/ton CO2 price
Table 2: Cost/standard deviation (left) and the correlation matrix (right)
Figure 2: The efficient frontier (left) and technology mix along the frontier (right)
In the second scenario, CO2 emission charge is at $40/ton. Nuclear is not affected
by this charge; higher CO2 price increases the generation cost of NGCC slightly and that
of coal much more. The cost range of the efficient portfolio shifts from $60 – 100/MWh
Cost/MWh S.D. Nuclear PC NGCC
Nuclear 106.75 2.20 Nuclear 1.00 0.11 -0.02 PC 93.42 5.53 PC 0.11 1.00 0.05 NGCC 68.82 14.03 NGCC -0.02 0.05 1.00
Nuclear
PC
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.9 71.5 74.1 76.8 79.4 82.0 84.6 87.3 89.9 92.5 95.1 97.8 100.4103.0
14.0 12.5 11.1 9.8 8.5 7.3 6.3 5.5 4.8 4.1 3.5 2.9 2.4 2.1
2 4 6 8 10 12 1465
70
75
80
85
90
95
100
105
110
NGCC
Cost ($/MWh)
S.D.
PC
Nuclear
Cost ($/MWh)
S.D.
PC
Nuclear
Cost ($/MWh)
S.D.
43
in the previous scenario to $69 – 104/MWh due to higher CO2 price charged to all fossil
fuel plants. NGCC has a more significant role gaining higher share especially in the first
half of the efficient frontier at the expense of PC because of its lower CO2 emission. The
cost difference between coal and gas increases from $13.6 to 24.6/MWh due to an
increase in CO2 price. Nuclear has a role similar to that is in the previous model. At a cost
of $80/MWh with standard deviation 8, the portfolio consists of 60% NGCC and 40%
PC.
• B3: Portfolio 7 technologies under $20/ton CO2 price
Table 3: Cost/standard deviation (left) and the correlation matrix (right)
Figure 3: The efficient frontier (left) and technology mix along the frontier (right)
In the 3rd scenario, 4 prospective future baseload technologies, IGCC, IGCC,
NGCC and PC with CCS are included in the portfolio. Nuclear is the highest cost
technology followed by PC CCS. NGCC and PC have significant share in the part of the
efficient portfolio frontier where portfolio cost is low and cost variation is high. For the
$/MWh S.D. Nuclear PC PC CCS IGCC IGCC CCS NGCC NGCC
CCS Nuclear 106.75 2.20 Nuclear 1.00 0.11 0.23 0.10 0.26 -0.02 -0.03 PC 73.42 5.53 PC 0.11 1.00 0.43 0.98 0.48 0.05 -0.07 PC CCS 101.68 4.17 PC CCS 0.23 0.43 1.00 0.41 0.85 -0.05 -0.03 IGCC 78.01 5.25 IGCC 0.10 0.98 0.41 1.00 0.52 0.02 -0.11 IGCC CCS 89.98 3.54
IGCC CCS 0.26 0.48 0.85 0.52 1.00 -0.05 -0.04
NGCC 59.82 14.03 NGCC -0.02 0.05 -0.05 0.02 -0.05 1.00 0.98 NGCC CCS 71.46 19.23
NGCC CCS -0.03 -0.07 -0.03 -0.11 -0.04 0.98 1.00
2 4 6 8 10 12 14 16 18 2050
60
70
80
90
100
110
S.D.
NGCC
PC
Nuclear
IGCC
IGCC CCS
PC CCS
NGCC CCS
S.D.
Cost ($/MWh)
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
59.9 63.3 66.6 70.0 73.3 76.6 80.0 83.3 86.7 90.0 93.3 96.7 100.0
13.9 11.4 9.1 7.0 5.6 5.0 4.5 4.1 3.8 3.4 3.2 2.9 2.6 2.4 2.2 2.1 2.0
44
higher cost portfolio, IGCC CCS starts to gain significant share. Although cost of IGCC
CCS is high, its volatility is lower than PC since there is volatility in future CO2 price.
The volatility in CO2 price increases the overall volatility of fossil fuel plants cost.
IGCC, NGCC CCS and PC CCS have no role in the optimal portfolio. IGCC has
higher cost and just lower volatility than PC. As a result, IGCC without CCS is a
dominated technology in our analysis. Also the cost of PC CCS is too high although its
volatility is less than PC. NGCC CCS is the second lowest cost technology but has the
highest volatility. NGCC CCS has higher volatility than NGCC because it uses more
natural gas due to higher heat rate. Thus, the volatility in natural gas price has more
impact on volatility of NGCC CCS generation cost. When forcing the portfolio to have
lower variance, more nuclear is required for the system. The lowest standard deviation
portfolio has about 70% nuclear capacity; its standard deviation of 2.0 is less than
nuclear’s (also the portfolio cost) due to the covariance of PC, IGCC CCS and NGCC
with nuclear. At $80/MWh portfolio cost with standard deviation 3.8, the optimal
portfolio consists of 5% Nuclear, 35% PC, 45% IGCC CCS and 15% NGCC.
• B4: Portfolio of 7 technologies under $40/ton CO2 price
Table 4: Cost/standard deviation (left) and the correlation matrix (right)
$/MWh S.D. Nuclear PC PC CCS IGCC IGCC CCS NGCC NGCC
CCS Nuclear 106.75 2.20 Nuclear 1.00 0.11 0.23 0.10 0.26 -0.02 -0.03 PC 93.42 5.53 PC 0.11 1.00 0.43 0.98 0.48 0.05 -0.07 PC CCS 103.68 4.17 PC CCS 0.23 0.43 1.00 0.41 0.85 -0.05 -0.03 IGCC 96.01 5.25 IGCC 0.10 0.98 0.41 1.00 0.52 0.02 -0.11 IGCC CCS 91.78 3.54
IGCC CCS 0.26 0.48 0.85 0.52 1.00 -0.05 -0.04
NGCC 68.82 14.03 NGCC -0.02 0.05 -0.05 0.02 -0.05 1.00 0.98 NGCC CCS 72.36 19.23
NGCC CCS -0.03 -0.07 -0.03 -0.11 -0.04 0.98 1.00
45
Figure 4: The efficient frontier (left) and technology mix along the frontier (right)
In the 4th scenario with $40/ton of CO2 price (figure 4), cost of technology with
high CO2 emission such as PC and IGCC increase significantly. NGCC is still the lowest
cost due to low CO2 emission per MWh. IGCC CCS replaces most of PC and some
nuclear from the previous scenario (B3). Share of PC decreases significantly due to
increase in cost from higher CO2 price. Nuclear again reduces portfolio variation but has
less significant role than the previous scenario. Like the previous scenario, there is no
share of IGCC, PC CCS and NGCC CCS in the optimal portfolio. At a cost of $80/MWh
with standard deviation around 5.2, the optimal portfolio consists of 45% IGCC CCS and
55% NGCC.
From the 4 scenarios in the baseline model, we can see that each generation
technology has different characteristic in term of cost and variation in cost. The nuclear
plant has high capital cost but low variable cost. Generation cost from nuclear does not
vary in high magnitude when uranium or operation cost change. Nuclear plays the same
role in all 4 scenarios to reduce the overall portfolio variation. However, because nuclear
is the highest cost technology more nuclear generation results in higher cost but lower
variation portfolio.
PC is the technology with moderate cost and cost variation. Emission of CO2 per
unit of power generation from PC is the highest among all technology. IGCC is also the
coal based technology with the high amount of CO2 emission. Cost of PC and IGCC are
highly sensitive to CO2 price and some of the cost variation of these 2 technologies is
attributed to the variation in CO2 price. PC CCS is another coal technology that emits
small amount of CO2. However, its cost is significantly higher than IGCC CCS with
Nuclear
PCIGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.9 71.6 74.3 77.1 79.8 82.5 85.3 88.0 90.7 93.4 96.2 98.9 101.6
14.0 12.7 11.5 10.2 9.0 7.8 6.7 5.6 4.6 3.8 3.4 3.1 2.8 2.5 2.3 2.1 2.0
2 4 6 8 10 12 14 16 18 2065
70
75
80
85
90
95
100
105
110
S.D.
Cost ($/MWh)
Cost ($/MWh)
S.D.
NGCC
PC
Nuclear
IGCC
IGCC CCS
PC CCS
NGCC CCS
46
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
3 Tech, $20/tonCO2
3 Tech, $40/tonCO2
7 Tech, $20/tonCO2
7 Tech, $40/tonCO2
IGCC CCSNGCCPCNuclear
about the same variation. Like IGCC, PC CCS is the dominated technology in this
analysis and has no share in the optimal portfolio.
NGCC is the low cost and high variance technology. NGCC has the high portion
of fuel cost in total generation cost; its generation cost is highly affected by the change in
natural gas price. NGCC can help lowering the portfolio cost in exchange for higher
variation. The CO2 price also increases the cost of NGCC but in lower magnitude than
PC and IGCC. NGCC CCS is another natural gas turbine technology with carbon capture
facility. Its cost is lower than some technologies but its variation is the highest. Note that
NGCC CCS uses higher amount of natural gas than NGCC due to its higher heat rate.
Technology shares along the efficient portfolio frontier are similar across these 4
scenarios. NGCC has a high share at the low cost-high variation portion of the frontier.
On the other hand, nuclear gains share at the high cost-low variation portion. PC and
IGCC CCS have some share along the frontier with the highest around the middle part of
the efficient set depending on the CO2 price.
When comparing portfolios with CO2 prices of $20 and $40/ton, significant
change can be observed especially from shares of the fossil fuel technology; NGCC, PC
and IGCC CCS. NGCC gains significant share when the system moves toward higher
CO2 price. It replaces most PC and some nuclear. When we introduce IGCC CCS in the
3rd and 4th scenarios, IGCC CCS seems to replace the share of PC rather than NGCC.
Shape of NGCC share is about the same after including IGCC CCS which can be seen by
comparing 1st with 3rd and 2nd with 4th scenarios.
Figure 5: Generation mix at $80/MWh
47
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
60 63 66 69 71 74 77 80 83 86 89 92 94 97 100Cost ($/MWh)
CO
2 (to
n/M
Wh)
14.0 11.1 8.5 6.3 5.2 4.8 4.4 4.0 3.7 3.3 3.0 2.7 2.4 2.2 2.1
S.D.
3 Tech @ CO2 $20/ton3 Tech @ CO2 $40/ton7 Tech @ CO2 $20/ton7 Tech @ CO2 $40/ton
When comparing all 4 scenarios and fixing the portfolio cost at $80/MWh, as seen
from Figure 5, the generation mixes are significantly different under the 2 CO2 prices.
For example, at a portfolio cost of $80/MWh, the 3-technology portfolio has about 25%
nuclear in $20/MWh CO2 price scenario but it has no nuclear when CO2 regulation cost
increases to $40/MWh. As new technologies are introduced to the 7-technology portfolio,
at $20/ton CO2 price, shares of NGCC is about the same but all shares of PC and some
nuclear are replaced by IGCC CCS. Also, at $40/ton CO2 all PC is replaced by IGCC
CCS. The change in portfolio mix is mainly due to the shift in portfolio cost and the
replacement of some nuclear and PC by IGCC CCS.
Figure 6: CO2 emission of the efficient portfolio
Figure 6 shows the amount of CO2 emission per MWh of the efficient portfolios
of the 3 and 7 technologies options under $20 and $40/ton of CO2 prices. Under $20/ton
CO2 price for 3 and 7-technology portfolios, the amount of CO2 increases at the
beginning due to the portfolio mix between NGCC and PC and reaches the peak at the
portfolio with the highest share of PC (as shown in Figure 2 and 4). When moving toward
the higher cost portfolio, nuclear and IGCC CCS (for 7-technology model) gain higher
share resulting in the reduction of CO2 emission. Under $20/ton CO2 price, portfolios
with 3 and 7 technologies have similar pattern of CO2 emission, it declines after reaching
the peak, but the 7-technology portfolios perform better in lowering CO2 emission at the
same level of cost and variation.
48
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
Nuclear
IGCC CCS
NGCC
NGCC CCS
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
73.2 75.5 77.8 80.1 82.4 84.7 87.0 89.3 91.6 93.9 96.1 98.4 100.7103.0
19.24 16.23 13.49 11.16 8.88 6.70 4.77 3.51 3.01 2.58 2.24 2.05
Nuclear
IGCC CCS
NGCC
NGCC CCS
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
74.2 76.6 79.1 81.5 84.0 86.4 88.8 91.3 93.7 96.1 98.6 101.0 103.5 105.9
19.19 16.78 14.38 12.01 9.67 7.43 5.37 3.83 3.15 2.62 2.23 2.03
In contrast, under $40/ton CO2 price, the patterns of CO2 emission between 3 and
7 technology portfolios are significantly different. CO2 emission under 3-technology
portfolio increases at the beginning and decreases as the portfolio moves to higher cost
and lower variance section. Unlike 3 technology portfolio, CO2 emission of 7 technology
portfolio decreases steadily due to higher share of IGCC CCS and nuclear as the portfolio
moves to higher cost and lower variance. As seen from the graph, introduction of IGCC
CCS helps lowering the CO2 emission at the given level of cost and variation compared
with the portfolio of current baseload technology.
The results from the baseline model indicate that some technologies such as PC
CCS and NGCC CCS are the dominated technologies in the optimal portfolio. These
technologies have higher cost than conventional technology but are insensitive to an
increase in CO2 price. The following analysis examines the change in portfolio mix if
significantly higher CO2 prices are imposed to the generator.
Figure 7: Portfolio of the baseline model with $60 (left) and $80/ton CO2 (right)
Figure 7 shows the portfolio mix when CO2 prices increase to $60 and $80/ton.
When CO2 prices are $60-80/ton, generation costs of all coal technology without CCS
increase to a level higher than nuclear. PC which almost disappears from the scenario
with $40/ton CO2 is not in the optimal portfolio. NGCC CCS becomes the lowest cost
technology with the highest variation.
The shares of IGCC CCS and nuclear are similar to the baseline model with
$40/ton CO2 price. The obvious change is between NGCC CCS and NGCC. When higher
CO2 prices are imposed, NGCC CCS has a large share in the optimal portfolio with low
cost-high variation similar to the role of NGCC in the baseline model. There are some
49
0
2
4
6
8
10
12
14
Jan-90
Apr-91
Jul-92
Oct-93
Jan-95
Apr-96
Jul-97
Oct-98
Jan-00
Apr-01
Jul-02
Oct-03
Jan-05
Apr-06
Jul-07
Oct-08
0
20
40
60
80
100
120
140
160
CoalNatural GasUranium
$/MBtu$/pound(uranium)
Stable price Volatile price
0
2
4
6
8
10
12
14
Jan-90
Apr-91
Jul-92
Oct-93
Jan-95
Apr-96
Jul-97
Oct-98
Jan-00
Apr-01
Jul-02
Oct-03
Jan-05
Apr-06
Jul-07
Oct-08
0
20
40
60
80
100
120
140
160
CoalNatural GasUranium
$/MBtu$/pound(uranium)
Stable price Volatile price
shares of NGCC under $60/ton CO2 price but at $80/ton it almost disappears from the
optimal portfolio. When $100/ton CO2 price is applied, the result is almost the same as
the model with $80/ton CO2 price.
2. Analysis of the fuel price structure
In this analysis, we divide the time period from 1990-2009 into 2 parts. Each one
represents a different structure of fuel price movement. The period from 1990-1999
represents the structure where fuel prices were stable (less volatile) called “the stable
price period”. The period from 2000- Jun 2009 represents the structure with high gas
price and volatility called “the volatile price period”. The figure below shows the
movement of real fuel price (in 2008 dollar) from 1990- Jun 2009.
Figure 8: Real fuel price movement from 1990-Jun 2009
50
Table 5: Correlation coefficients of fuel prices in 2 price structures
From table 5, the correlation coefficients of fuel prices differ in the 2 periods. In
the ‘stable price’ structure, prices of all fuels are stable (low standard deviation). The
correlation coefficient between uranium and natural gas is positive but those with coal
price are negative. In the ‘volatile price’ structure, all fuel prices are positively correlated.
Uranium price has the highest fluctuation and increases sharply during the volatile price
period. Note that although uranium has the highest standard deviation, the nuclear power
generation process uses small amount of uranium per MWh resulting in low standard
deviation of nuclear generation cost.
The model includes the same set of 7 technologies as in the baseline model. The
optimal portfolio frontier is solved separately for each fuel price structure under CO2
prices of $20 and 40/ton. Note that the correlation coefficient of the fuel cost and that of
the total generation cost may not represent the same structure of correlation. The
generation cost includes other cost components such as O&M and CO2 regulation cost.
• Stable price period (1990-1999) at $20/ton CO2 price
Table 6: Cost/standard deviation (left) and the correlation matrix (right)
1990-1999 2000-Jun 2009
Uranium Coal Gas Uranium Coal Gas
Uranium 1.00 -0.21 0.23 Uranium 1.00 0.78 0.42 Coal -0.21 1.00 0.10 Coal 0.78 1.00 0.35 Gas 0.23 0.10 1.00 Gas 0.42 0.35 1.00
Mean 14.31 1.82 3.29 Mean 38.62 1.67 6.65 S.D. 2.56 0.22 0.51 S.D. 33.39 0.24 2.07
$/MWh S.D. Nuclear PC PC CCS IGCC IGCC CCS NGCC NGCC
CCS Nuclear 107.32 2.03 Nuclear 1.00 -0.23 -0.44 -0.26 -0.40 0.13 0.10 PC 73.62 5.16 PC -0.23 1.00 0.55 0.97 0.46 0.32 0.04 PC CCS 102.49 4.23 PC CCS -0.44 0.55 1.00 0.57 0.83 0.16 0.25 IGCC 78.43 4.73 IGCC -0.26 0.97 0.57 1.00 0.55 0.28 0.03 IGCC CCS 90.69 3.28
IGCC CCS -0.40 0.46 0.83 0.55 1.00 0.09 0.26
NGCC 50.23 4.14 NGCC 0.13 0.32 0.16 0.28 0.09 1.00 0.81 NGCC CCS 57.35 4.80
NGCC CCS 0.10 0.04 0.25 0.03 0.26 0.81 1.00
51
Figure 9: Technology mix along the efficient frontier
The optimal portfolio in this scenario is dominated by NGCC. Cost difference
between NGCC and other technologies is large. In addition, standard deviation of NGCC
cost is not relatively high. This is due to the stable movement of the natural gas price in
this period. Note that PC and IGCC have high standard deviation partially due to the
volatility of the simulated CO2 price. The capacity share of PC is small and there is no
share of IGCC in the optimal portfolio. The share of IGCC CCS is stable; about 25-30%
along the efficient frontier. Like other scenarios portfolio, nuclear dominates the
technology mix in the higher cost and lower variation portion of the efficient frontier.
The largest share of nuclear on the efficient portfolio is around 60%. In this scenario, it
seems that the change in portfolio mix along the frontier is mainly between NGCC and
nuclear, since share of IGCC CCS and PC are quite stable. At portfolio cost $80/MWh,
the optimal portfolio consists of 35% nuclear, 2% PC, 23% IGCC CCS and 40% NGCC.
• Stable price period (1990-1999) at $40/ton CO2 price
Table 7: Cost/standard deviation (left) and the correlation matrix (right)
$/MWh S.D. Nuclear PC PC CCS IGCC IGCC CCS NGCC NGCC
CCS Nuclear 107.32 2.03 Nuclear 1.00 -0.23 -0.44 -0.26 -0.40 0.13 0.10
PC 93.62 5.16 PC -0.23 1.00 0.55 0.97 0.46 0.32 0.04 PC CCS 104.49 4.23 PC CCS -0.44 0.55 1.00 0.57 0.83 0.16 0.25 IGCC 96.43 4.73 IGCC -0.26 0.97 0.57 1.00 0.55 0.28 0.03 IGCC CCS 92.49 3.28 IGCC
CCS -0.40 0.46 0.83 0.55 1.00 0.09 0.26
NGCC 59.23 4.14 NGCC 0.13 0.32 0.16 0.28 0.09 1.00 0.81 NGCC CCS 58.25 4.80 NGCC
CCS 0.10 0.04 0.25 0.03 0.26 0.81 1.00
S.D.
Cost ($/MWh)
NuclearPC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
50.3 53.6 57.0 60.4 63.8 67.2 70.6 74.0 77.4 80.8 84.2 87.5 90.9 94.3 97.7
4.14 3.82 3.53 3.27 3.04 2.81 2.58 2.36 2.15 1.96 1.78 1.62 1.49 1.39 1.34
52
S.D.
Cost ($/MWh)
Nuclear
PC
IGCC CCS
NGCC
NGCC CCS
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
58.3 61.2 64.1 67.1 70.0 72.9 75.9 78.8 81.8 84.7 87.6 90.6 93.5 96.4 99.4
4.80 3.90 3.59 3.32 3.07 2.84 2.60 2.38 2.16 1.96 1.78 1.61 1.48 1.39 1.34
Figure 10: Technology mix along the efficient frontier
The optimal portfolio in this case is similar to the previous one except that the
range of the efficient frontier is shifted due to the higher CO2 charge. NGCC still
dominates in this scenario because it has low cost, moderate volatility and low CO2
emission. In addition there are some shares of NGCC CCS at the lower portion of the
frontier. NGCC CCS has just lower cost than NGCC with slightly higher volatility. The
share of IGCC CCS is quite stable along the frontier. It increases steadily from the low
cost portfolio and becomes constant at around 25-30%. At cost $80/MWh, the optimal
portfolio consists of 25% nuclear, 30% IGCC CCS and 45% NGCC.
This $20/ton increase in CO2 price does not significantly change the results in the
‘stable price’ scenario. Only NGCC CCS appears in the optimal portfolio when higher
CO2 price is charged. The key technologies are NGCC, IGCC CCS and Nuclear. NGCC
and NGCC CCS account for large percentage in the low cost and high variation part of
the efficient frontier. Similarly, nuclear dominates the high cost and low variance
portfolios.
53
S.D.
Cost ($/MWh)
NuclearPC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
69.6 72.4 75.2 78.0 80.8 83.6 86.4 89.2 92.0 94.8 97.6 100.4 103.2
14.0 6.0 5.0 4.6 4.3 4.0 3.8 3.6 3.4 3.2 3.0 2.8 2.7 2.5 2.4 2.3 2.2
• Volatile price period (2000-2009) at $20/ton CO2 price
Table 8: Cost/standard deviation (left) and the correlation matrix (right)
Figure 11: Technology mix along the efficient frontier
In this scenario, the technologies that dominates the optimal portfolio are PC and
nuclear. Natural gas price in this case is high and volatile. Although, NGCC is still the
lowest cost technology but the cost difference between NGCC and other technology is
smaller than the previous scenario. Shares of NGCC are high for a short portion of the
efficient frontier and decrease sharply. PC dominates most of the low cost/high variance
part of the efficient portfolios. IGCC CCS gains significant share in the middle portion of
the efficient frontier with the highest share around 45%. Like other scenarios, nuclear
plays a key role in the high cost portion of the portfolio frontier. There are no share of
IGCC, PC CCS and NGCC CCS in the optimal portfolio. At cost $80/MWh, the optimal
portfolio consists of 45% IGCC CCS, 50% PC and 5% NGCC.
$/MWh S.D. Nuclear PC PC CCS IGCC IGCC CCS NGCC NGCC
CCS Nuclear 106.16 2.22 Nuclear 1.00 0.35 0.66 0.32 0.67 0.30 0.35 PC 72.53 5.41 PC 0.35 1.00 0.43 0.97 0.48 0.17 0.07 PC CCS 100.46 4.25 PC CCS 0.66 0.43 1.00 0.38 0.83 0.23 0.29 IGCC 76.94 5.05 IGCC 0.32 0.97 0.38 1.00 0.52 0.17 0.07 IGCC CCS 89.01 3.82
IGCC CCS 0.67 0.48 0.83 0.52 1.00 0.23 0.28
NGCC 69.62 13.96 NGCC 0.30 0.17 0.23 0.17 0.23 1.00 0.98 NGCC CCS 86.20 17.88
NGCC CCS 0.35 0.07 0.29 0.07 0.28 0.98 1.00
54
S.D.
Cost ($/MWh)
Nuclear
PCIGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
78.7 80.8 83.0 85.1 87.3 89.5 91.6 93.8 96.0 98.1 100.3 102.5 104.6
13.9 12.2 10.5 8.8 7.2 5.8 4.6 3.8 3.6 3.4 3.1 2.9 2.8 2.6 2.4 2.3 2.2
• Volatile price period (2000-2009) at $40/ton CO2 price
Table 9: Cost/standard deviation (left) and the correlation matrix (right)
Figure 12: Technology mix along the efficient frontier
In this scenario, IGCC CCS dominates the optimal technology mix portfolio
especially in the middle part of the efficient frontier. NGCC is still the lowest cost
technology and the gap of generation cost with PC and IGCC is larger due to higher CO2
price. NGCC gains more shares in the low cost portion of the portfolio than the previous
scenario due to low CO2 price. IGCC CCS has significant influence along the frontier.
This is due to cost advantage over PC and IGCC when higher CO2 regulation cost is
charged. At cost $80/MWh, the optimal portfolio consists of 20 % IGCC CCS and 80%
NGCC.
This analysis shows that the period of the historical fuel cost to be used in the
analysis can determine the result. The planner can choose the period which he believes
$/MWh S.D. Nuclear PC PC CCS IGCC IGCC CCS NGCC NGCC
CCS Nuclear 106.16 2.22 Nuclear 1.00 0.35 0.66 0.32 0.67 0.30 0.35 PC 92.53 5.41 PC 0.35 1.00 0.43 0.97 0.48 0.17 0.07 PC CCS 102.46 4.25 PC CCS 0.66 0.43 1.00 0.38 0.83 0.23 0.29 IGCC 94.94 5.05 IGCC 0.32 0.97 0.38 1.00 0.52 0.17 0.07 IGCC CCS 90.81 3.82
IGCC CCS 0.67 0.48 0.83 0.52 1.00 0.23 0.28
NGCC 78.62 13.96 NGCC 0.30 0.17 0.23 0.17 0.23 1.00 0.98 NGCC CCS 87.10 17.88
NGCC CCS 0.35 0.07 0.29 0.07 0.28 0.98 1.00
55
best represents the future structure. The components that account for these differences are
the expected generation cost, variation and correlation of the cost between technologies.
3. Analysis of expected future fuel price
The baseline model used the expected power generation cost calculated from the
historical fuel cost data. In this analysis, we assume that the distribution of future fuel
cost is the same as the historical distribution during 1990-2009. The efficient portfolio
frontier is formulated under different values for the natural gas and coal prices.
The expected price of natural gas in the baseline model is $4.8/Mcf (Million cubic
feet). The expected future price of natural gas used in this analysis is $6 and $10/Mcf.
The Annual Energy Outlook 2010 by EIA (2009) forecasts the price of natural gas for the
electric power sector to be at the range from $6 – $9/Mcf (2008 dollars) during the next
25 years. At $20/ton CO2 price, NGCC costs are $68.6 and $97.5/MWh for natural gas
prices at $6 and 10$/Mcf respectively. In addition, at $40/ton CO2 price, the costs of
NGCC are $77.6 and $106.5/MWh for natural gas price at $6 and 10$/Mcf respectively.
Figure 13 below shows the technology mix along the efficient portfolio frontier under
different scenarios of natural gas and CO2 prices.
a) $6/Mcf and $20/ton CO2 price b) $6/Mcf and $40/ton CO2 price
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
NuclearPC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.6 71.3 73.9 76.6 79.2 81.9 84.6 87.2 89.9 92.5 95.2 97.9 100.5
18.0 10.8 5.6 5.0 4.6 4.2 3.9 3.6 3.4 3.1 2.9 2.7 2.5 2.3 2.2 2.1 2.0
Nuclear
PCIGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
77.7 79.8 81.8 83.9 85.9 88.0 90.0 92.1 94.2 96.2 98.3 100.3 102.4
17.8 15.8 13.9 11.9 10.0 8.2 6.4 4.8 3.7 3.3 3.0 2.8 2.6 2.4 2.2 2.1 2.0
56
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
73.4 75.7 78.0 80.3 82.7 85.0 87.3 89.6 91.9 94.2 96.5 98.8 101.1
5.52 5.09 4.69 4.32 4.00 3.73 3.47 3.22 2.98 2.76 2.56 2.38 2.23 2.12 2.05
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
91.8 92.7 93.7 94.6 95.6 96.6 97.5 98.5 99.4 100.4 101.4 102.3 103.3
3.54 3.35 3.20 3.05 2.91 2.77 2.65 2.53 2.41 2.32 2.23 2.16 2.10 2.06 2.03
c) $10/Mcf and $20/ton CO2 price d) $10/Mcf and $40/ton CO2 price
Figure 13: Optimal portfolio mix under different natural gas and CO2 price
Since the fuel cost accounts for large portion of power generation from NGCC, an
increase in fuel cost affects the total generation cost significantly. When the natural gas
price is at $6/Mcf, NGCC has a significant share when portfolio variance is high but, its
share decreases sharply compared with the baseline model as we lower portfolio standard
deviation.
As the price of natural gas increases to $10/Mcf, there is almost no NGCC in the
optimal portfolio; the share is less than 1%. At low CO2 price, the efficient portfolio
mainly consists of PC, IGCC CCS and nuclear. However, when CO2 price is high, IGCC
CCS and nuclear dominate the portfolio. Note that the optimal portfolio mix is the same
when natural gas price is at $16/Mcf; it is the dominated technology since NGCC has
high cost and high volatility.
Figure 14 shows the optimal technology mix of the efficient portfolio at $2/Mbtu
coal and $10/Mcf natural gas. Note that the baseline price of coal is at $1.7/Mbtu and the
forecast coal price in EIA (2009) is around $2/Mbtu over the next 25 years.
57
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
75.8 78.0 80.2 82.4 84.6 86.8 89.0 91.2 93.4 95.6 97.8 100.0 102.2
5.63 5.24 4.88 4.55 4.25 3.96 3.67 3.40 3.13 2.89 2.66 2.46 2.29 2.17 2.08
NuclearPC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
94.5 95.3 96.1 97.0 97.8 98.6 99.4 100.2 101.1 101.9 102.7 103.5 104.3
3.81 3.60 3.43 3.26 3.10 2.94 2.79 2.65 2.52 2.40 2.30 2.21 2.14 2.09 2.06
a) Gas at $6/Mcf and CO2 at $20/ton b) Gas at $6/Mcf and CO2 at $40/ton
c) Gas at $10/Mcf and CO2 at $20/ton d) Gas at $10/Mcf and CO2 at $40/ton
Figure 14: Optimal portfolio mix at $2/Mbtu coal price and $6 and 10/Mcf gas price
With $2/Mbtu coal price and $6/Mcf natural gas price, the optimal portfolio mix
is similar to the baseline model but when gas price is at $10/Mcf, the optimal technology
mix is different. Especially, when CO2 price is at $20/ton, PC dominates the portfolio
frontier at low cost and high variance portion and the high cost and low variance portion
is dominated by nuclear. However, when cost of CO2 is higher, the optimal technology
mix is similar to Figure 13 (d) where IGCC CCS and nuclear dominates the whole
efficient portfolio.
The decision rule to choose the optimal technology mix of the planner or utility
can be based on the marginal rate of substitution (MRS) between cost and variation in
cost. Theoretically, the selection of the optimal portfolio depends on the utility function
of the planner. In this study, the decision rule is simplified such that the planner decides
the MRS between cost and variation and chooses the portfolio that satisfies that
condition. For example, the MRS of $5/MWh/S.D. can be interpreted that the planner is
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
Nuclear
PC
IGCC CCSNGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.6 71.4 74.1 76.8 79.6 82.3 85.1 87.8 90.5 93.3 96.0 98.8 101.5
18.0 12.3 7.4 5.3 4.9 4.5 4.1 3.8 3.5 3.1 2.9 2.6 2.4 2.2 2.1
NuclearPC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
77.6 79.8 81.9 84.0 86.2 88.3 90.4 92.6 94.7 96.9 99.0 101.1 103.3
18.0 16.2 14.5 12.8 11.1 9.5 7.9 6.4 5.0 4.0 3.6 3.2 2.9 2.6 2.3 2.2 2.1
58
Baseline ($4.8/Mcf) $10/Mcf$6/Mcf Gas Price
CO2 cost ($/ton)
20
40
NGCC14%
PC56%IGCC CCS
30%
NGCC11%
IGCC CCS68%
Nuclear17%
PC4%
NGCC7%
IGCC CCS36%
PC57%
NGCC6%
IGCC CCS71%
Nuclear17%
PC6%
NGCC1%
PC59%
IGCC CCS39.5%
NGCC1%
Nuclear25%
IGCC CCS66.7% PC
7%
willing to increase power generation cost by $5/MWh for the reduction of 1 standard
deviation of the portfolio.
MRS $/MWh SD Nuclear PC PC CCS IGCC IGCC
CCS NGCC NGCC CCS
3 70.27 5.48 0.0% 76.8% 0.0% 0.0% 0.0% 23.2% 0.0% 4 70.65 5.37 0.0% 79.7% 0.0% 0.0% 0.0% 20.3% 0.0% 5 72.58 4.97 0.0% 73.1% 0.0% 0.0% 9.4% 17.6% 0.0% 6 76.50 4.26 0.0% 55.1% 0.0% 0.0% 30.5% 14.4% 0.0% 7 78.50 3.95 0.0% 45.9% 0.0% 0.0% 41.2% 12.8% 0.0% 8 80.80 3.65 4.1% 38.8% 0.0% 0.0% 45.6% 11.4% 0.0% 9 86.28 3.00 23.4% 29.6% 0.0% 0.0% 38.1% 9.0% 0.0% 10 89.09 2.71 33.2% 24.8% 0.0% 0.0% 34.2% 7.8% 0.0%
Table 10: Optimal portfolio mix at different MRS
Table 10 shows the optimal portfolio under the baseline model with $20/ton of
CO2 price at different MRS. As the MRS increases, the optimal portfolio moves toward
the lower variance portfolio (also with higher cost). In other words, higher MRS means
more risk aversion. Given the marginal rate of substitution (MRS), the optimal
technology mix can vary significantly depending on the scenario on generation cost as
shown in figure 15.
Figure 15: The optimal portfolio mix at the MRS of $5/MWh/S.D.
The scenario of fuel and CO2 price that the planner uses for deciding the
technology mix and the actual event could be different. Although demand grows every
year but the new generation capacity could not change the overall technology mix
59
0.00
10.00
20.00
30.00
40.00
Baseline($4.8/Mcf)
$6/Mcf $10/Mcf $16/Mcf
$/MWh
At 20 CO2 (Low MRS)At 40 CO2 (Low MRS)At 20 CO2 (High MRS)At 40 CO2 (High MRS)
significantly. The selected portfolio could have different cost and variation if the referred
scenario does not happen.
Figure 16: Regret graph from decision at the baseline cost at the MRS of $3 and
$8/MWh/S.D.
We define the term ‘regret’ as the change in portfolio cost if the planned scenario
does not occur. Positive regret means that the portfolio cost is higher when another
scenario occurs. Figure 16 shows the regret graph of the portfolio mix based on the
decision at the baseline scenario with $20/ton CO2 price. The figure shows results from 2
MRS; $3 and $8/MWh/S.D. If the planner is concerned more about variance (at $8/S.D.),
the portfolio has higher cost but lower standard deviation and less ‘regret’ than at $3/S.D.
In addition, there are more shares of IGCC CCS and nuclear under MRS $8/S.D. which
reduces the impact of unexpected higher CO2 price and natural gas cost.
4. Analysis of the capital cost
Various published reports show different capital cost for each technology. The
actual capital cost especially for the future technology is generally unobservable.
Manufacturing and construction of the power plant require similar resources for example
steel, cement and labor. Figure 17 shows the construction cost index (Handy-Whitman
60
90
100
110
120
130
140
150
160
170
1996 1998 2000 2002 2004 2006 2008
Steam Turbine PlantNuclear PlantGas Turbine PlantChemical Eng. Plant
Index) of 3 power plant technologies including nuclear, steam turbine and gas turbine
power plant and chemical engineering plant index.
Currently there are not many IGCC plants operating and the capital cost is
uncertain. However, an IGCC plant is a combination of a chemical plant (a gasification
unit) and power plant (a gas turbine). The chemical engineering plant index and gas
turbine index together can represent IGCC plant construction cost index.
Data source: Handy-Whitman index and Chemical Engineering (2003, 2009)
Figure 17: Power plant related construction cost index (1996=100)
Over the 12 years from 1996-2008 the 3 indices are almost identical. The
anomalous gas turbines during 2004-2005 can be explained by the precipitous drop in
demand for these plants. Chupka and Basheda (2007) discussed recent increase in utility
construction costs. Various index, other than four index shown in Figure 17, such as
labor, steel/metal, manufacturing and heavy construction cost increase altogether. Since
construction of all power plant types uses common resources, we can imply that cost
generally move up and down together.
In this section, we test how the portfolio mix along the efficient frontier changes
when the capital cost changes. We impose a ± 30% change in capital cost for each
technology. Note that the percentage change in power generation cost ($/MWh) of each
technology is not the same since some technologies are more capital intensive. A ± 30%
change in capital cost changes the generation cost of nuclear by ± 22%; for PC, IGCC
61
and IGCC CCS, the change is ± 11-14%. For NGCC and NGCC CCS, the cost changes
only by ± 4-8% since capital cost accounts for a smaller proportion than other
technologies.
$20/ton CO2 $40/ton CO2 Cost ($/MWh)
Baseline -30% +30% Baseline -30% +30%
Nuclear 106.75 83.41 130.10 106.75 83.41 130.10 PC 73.42 65.48 81.36 93.42 85.48 101.36
PC CCS 101.68 88.52 114.84 103.68 90.52 116.84 IGCC 78.01 68.82 87.20 96.01 86.82 105.20
IGCC CCS 89.98 77.24 102.72 91.78 79.04 104.52 NGCC 59.82 57.43 62.22 68.82 66.43 71.22
NGCC CCS 71.46 65.80 77.12 72.36 66.70 78.02
Table 11: Generation cost as capital cost varies
The efficient portfolio mix of these of the tested scenario is shown in figure 18.
The ranges of the efficient portfolio are different due to the change in capital cost. The
role of each technology mix along the frontier is similar to the baseline model. In
addition, the significant change only occurs between PC and IGCC CCS. Shape of
NGCC and nuclear portfolio mix does not change from the baseline scenario.
a) Capital cost decreases 30%
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
Nuclear
PC
IGCC CCSNGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
57.4 58.9 60.4 61.9 63.4 64.9 66.4 67.9 69.4 70.9 72.4 73.9 75.4 76.9 78.4 79.9
14.0 11.6 9.4 7.4 5.8 5.2 4.8 4.4 4.0 3.7 3.3 3.0 2.7 2.5 2.3 2.1 2.0
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
66.4 67.5 68.5 69.5 70.5 71.5 72.6 73.6 74.6 75.6 76.6 77.7 78.7 79.7 80.7 81.7
14.0 12.9 11.9 10.8 9.7 8.7 7.7 6.7 5.7 4.9 4.1 3.6 3.1 2.7 2.4 2.1 2.0
62
b) Baseline capital cost
c) Capital cost increases 30%
Figure 18: Efficient portfolio mix at $20 (left) and $40/ton CO2 (right)
Figure 19 below shows the share of all technologies along the efficient frontier.
In order to compare 2 scenarios, in each figure the efficient frontier is normalized to be
on the same horizontal axis. At $20/ton CO2 price, the change in technology mix occurs
mainly with IGCC CCS and PC. When capital cost increases, some of PC share is
replaced by IGCC CCS. The opposite occurs when capital cost increases. At $40/ton CO2
price, when the capital cost decreases most of PC share is replaced by IGCC CCS and
NGCC. There is almost no share of PC when capital decreases by 30%. Also, when
capital cost increases, the change is opposite.
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
62.2 67.0 71.8 76.6 81.4 86.2 90.9 95.7 100.5 105.3 110.1 114.9 119.6
14.0 11.5 9.1 7.0 5.6 4.9 4.4 4.0 3.6 3.4 3.1 2.8 2.6 2.4 2.2 2.1 2.0
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
71.2 75.4 79.6 83.7 87.9 92.1 96.2 100.4 104.6 108.7 112.9 117.0 121.2
14.0 12.6 11.2 9.9 8.6 7.4 6.2 5.1 4.2 3.5 3.2 2.9 2.7 2.4 2.2 2.1 2.0
S.D.
Cost ($/MWh)
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
59.9 63.3 66.6 70.0 73.3 76.6 80.0 83.3 86.7 90.0 93.3 96.7 100.0
13.9 11.4 9.1 7.0 5.6 5.0 4.5 4.1 3.8 3.4 3.2 2.9 2.6 2.4 2.2 2.1 2.0
Nuclear
PCIGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.9 71.6 74.3 77.1 79.8 82.5 85.3 88.0 90.7 93.4 96.2 98.9 101.6
14.0 12.7 11.5 10.2 9.0 7.8 6.7 5.6 4.6 3.8 3.4 3.1 2.8 2.5 2.3 2.1 2.0S.D.
Cost ($/MWh)
63
Figure 19: Portfolio at ±30% change in capital cost at $20 (left) and $40/ton CO2 price
Nuclear (-30%)
PC (-30%)
IGCC CCS (-30%)
NGCC (-30%)
Nuclear (+30%)
PC (+30%)
IGCC CCS (+30%)NGCC (+30%)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Along the efficient frontier
Nuclear (-30%)
PC (-30%)
IGCC CCS (-30%)
NGCC (-30%)
Nuclear (+30%)PC (+30%)
IGCC CCS (+30%)
NGCC (+30%)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Along the efficient frontier
-30% 30%
0%
10%
20%
30%
40%
50%
60%
70%
80%
Along the efficient frontier
-30%30%
0%
10%
20%
30%
40%
50%
60%
70%
80%
Along the efficient frontier
-30%30%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
Along the efficient frontier
-30%-20% -10%
Baseline10%
20%
30%
0%
5%
10%
15%
20%
25%
30%
35%
40%
Along the efficient frontier
-30%
-20%
-10%
Baseline10%
20%
30%
0%
10%
20%
30%
40%
50%
Along the efficient frontier
-30%
30%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
Along the efficient frontier
Nuclear
PC
IGCC CCS
64
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
Nuclear
PC
IGCC CCSNGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
55.8 56.6 57.3 58.0 58.8 59.5 60.2 61.0 61.7 62.4 63.2 63.9 64.7 65.4 66.1 66.9
14.0 11.9 9.8 7.9 6.3 5.4 4.9 4.5 4.1 3.7 3.4 3.0 2.7 2.4 2.2 2.1 2.0
Nuclear
PC
IGCC CCS
NGCC
NGCC CCS
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
64.8 65.1 65.4 65.6 65.9 66.1 66.4 66.7 66.9 67.2 67.4 67.7 68.0 68.2 68.5 68.7
11.8 10.8 9.9 8.9 8.0 7.1 6.1 5.2 4.4 3.6 2.8 2.3 2.1 2.1 2.0 2.0 2.0
Figure 20: Share of each technology under changes in capital cost at $20 (left) and
$40/ton CO2 price (right)
The analysis shows that when all capital cost moves together there is no
significant change in the pattern of the portfolio mix. There are significant changes
between some technologies, PC and IGCC CCS. These 2 technologies are the
technologies in the middle portion of the efficient frontier. With moderate change at
±30%, there is no change in the cost order of the technology at the boundary.
However, as shown in figure 21, when the change is more extreme for example at
50% decrease in capital cost, portfolio mix changes significantly. In this case, nuclear is
not the highest cost technology and the gap between NGCC and NGCC CCS cost is
smaller. At $20/ton CO2 price, PC and nuclear dominate most part of the portfolio and
there is only small share of IGCC CCS. When CO2 price increases, nuclear dominates the
portfolio since cost of all fossil fuel technology is higher. Also, NGCC CCS replaces
NGCC at the low cost and high volatility portfolios.
Figure 21: Mix at 50% capital cost decreases at $20 (left) and $40/ton CO2 price (right)
-30%30%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Along the efficient frontier
-30%30%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Along the efficient frontier
NGCC
65
In the previous analysis, the efficient portfolio is formulated under the same
percentage change in capital cost for all technologies. In this analysis, we assume a
change in capital cost of specific technologies relative to the baseline value. Since the
capital cost has the range of possible value, we perform a sensitivity analysis at ± 30%
capital cost range for nuclear, IGCC and IGCC CCS.
− Analysis of nuclear capital cost
We perform another analysis where only nuclear capital cost changes ±30% from
the baseline value. Table 12 shows the generation cost from nuclear from different
percentages change in the capital cost.
Change in capital cost
Nuclear cost ($/MWh)
% Change in generation cost
-30% 83.41 -22% -20% 91.19 -15% -10% 98.97 -7%
Baseline 106.75 - 10% 114.54 7% 20% 122.32 15% 30% 130.10 22%
Table 12: Generation cost of nuclear at different capital cost levels
a) 30% decrease in nuclear capital cost
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
59.8 61.3 62.8 64.4 65.9 67.4 68.9 70.4 71.9 73.4 74.9 76.4 78.0 79.5 81.0 82.5
14.0 12.6 11.2 9.8 8.6 7.4 6.4 5.6 5.1 4.5 4.0 3.4 3.0 2.6 2.3 2.1 2.0
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.8 69.9 70.9 71.9 73.0 74.0 75.1 76.1 77.1 78.2 79.2 80.2 81.3 82.3 83.3 84.4
14.0 13.1 12.1 11.2 10.2 9.3 8.4 7.5 6.5 5.6 4.8 3.9 3.2 2.6 2.2 2.1 2.0
66
b) 30% increase in nuclear capital cost
Figure 22: Portfolio at different nuclear capital cost at $20 (left) and $40/ton CO2 (right)
Under low nuclear capital cost scenario, the share of nuclear replaces the share of
IGCC CCS compared with the baseline model. Some shares of IGCC CCS are also
replaced by PC and NGCC. When CO2 price is high, NGCC and nuclear are the only
dominant technologies; IGCC CCS does not play a significant role as in the baseline
model. For high nuclear cost scenario, the shape of the portfolio is similar to the baseline
model with extended range of the efficient frontier.
With carbon costs at $20-$40/ton, IGCC CCS and nuclear are direct competitor.
Low nuclear costs crowd out IGCC CCS and vice versa. Figure 23 and figure 24 show
share of nuclear and IGCC CCS in all scenarios. Shares of nuclear and IGCC CCS
change in the opposite direction as the capital cost of nuclear changes. IGCC CCS has
lowered share in the optimal portfolio when nuclear cost is lower.
Figure 23: Nuclear share along the efficient frontier at different levels of nuclear capital
cost with $20 (left) and $40/ton CO2 (right)
-30%-20%
Baseline
30%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
Along the efficient frontier
-30%
-20%
-10%
Baseline10%20%
30%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Along the efficient frontier
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
NuclearPC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
59.8 64.6 69.3 74.1 78.8 83.6 88.3 93.1 97.8 102.6 107.3 112.1 116.8
14.0 10.5 7.4 5.4 4.7 4.1 3.6 3.4 3.1 2.9 2.7 2.6 2.4 2.3 2.1 2.1 2.0
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.8 73.0 77.1 81.3 85.4 89.6 93.7 97.9 102.1 106.2 110.4 114.5 118.7
14.0 12.1 10.2 8.4 6.6 5.0 3.8 3.3 3.1 2.9 2.7 2.5 2.4 2.2 2.1 2.1 2.0
67
Figure 24: IGCC CCS share along the efficient frontier at different levels of nuclear
capital cost with $20 (left) and $40/ton CO2 (right)
− Analysis of IGCC and IGCC CCS total plant cost
We analyze the change in the share of IGCC and IGCC CCS when capital cost of
both technology changes. Since IGCC and IGCC CCS have almost the same facility
except the CCS unit, we assume the same percentage change of both technologies in each
case. Capital costs of other technology are assumed to be at the baseline level. The test
percentage change is between ± 30% of the baseline value. Table 13 below shows the
change in generation cost at different levels of change in capital cost.
$20/ton CO2
$40/ton CO2
Change in capital cost IGCC IGCC CCS IGCC IGCC CCS
-30% 68.82 (-12%) 77.24 (-14%) 86.82 (-10%) 79.04 (-14%) -20% 71.88 (-8%) 81.48 (-9%) 89.88 (-6%) 83.28 (-9%) -10% 74.94 (-4%) 85.73 (-5%) 92.94 (-3%) 87.53 (-5%)
Baseline 78.01 89.98 96.01 91.78 10% 81.07 (4%) 94.22 (5%) 99.07 (3%) 96.02 (5%) 20% 84.13 (8%) 98.47 (9%) 102.13 (6%) 100.27 (9%) 30% 87.2 (12%) 102.72(14%) 105.2 (10%) 104.52 (14%)
Note: percentage change in total generation cost in the parenthesis
Table 13: Cost/MWh at different capital cost of IGCC and IGCC CCS
From the baseline model, the result shows that the share of IGCC CCS increases
significantly when moving from $20 to $40/ton CO2 price. Cost of IGCC CCS becomes
more competitive compared with other fossil fuel technology especially PC.
-30%-20%
-10%
Baseline
10%
20%30%
0%
10%
20%
30%
40%
50%
60%
70%
Along the efficient frontier
-30%-20%
-10%Baseline10%
20%30%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
Along the efficient frontier
68
a) IGCC/ IGCC CCS capital cost decreases by 30%
b) IGCC/ IGCC CCS capital cost increases by 30%
Figure 25: Efficient portfolio mix at different levels of IGCC and IGCC CCS
capital cost at $20 (left) and $40/ton CO2 price
Figure 26 shows the share of IGCC CCS along the efficient portfolio frontier at 2
levels of CO2 price. Note that at each level of CO2 price, the range of the efficient frontier
is approximately the same for all scenarios of IGCC cost since there is no change in the
cost of NGCC and nuclear which at the high and low end of the frontier. At $20/ton CO2
price, the share of IGCC increases steadily as the capital cost lowered; it replaces PC and
there is no significant change in NGCC share. However as the capital cost increases,
especially from 20-30%, the share of IGCC CCS almost disappears from the efficient
portfolio.
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
NuclearIGCC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
59.8 62.7 65.5 68.4 71.3 74.1 77.0 79.8 82.7 85.5 88.4 91.2 94.1 97.0
14.02 9.55 5.91 4.49 3.70 3.32 3.06 2.82 2.60 2.40 2.24 2.12 2.04 2.01
Nuclear
IGCCIGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.8 70.8 72.8 74.8 76.8 78.8 80.8 82.8 84.8 86.8 88.8 90.8 92.8 94.8 96.8 98.8
14.02 10.69 7.48 4.66 3.36 3.13 2.90 2.69 2.50 2.34 2.20 2.10 2.03 2.01
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
Nuclear
PC
IGCC CCSNGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
59.8 63.4 66.9 70.4 74.0 77.5 81.0 84.6 88.1 91.6 95.1 98.7 102.2
14.0 11.4 8.9 6.8 5.4 5.0 4.6 4.3 3.9 3.6 3.2 2.9 2.7 2.4 2.2 2.1 2.0
Nuclear
PC
IGCC CCSNGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.8 71.8 74.7 77.6 80.6 83.5 86.4 89.4 92.3 95.2 98.2 101.1 104.0
14.0 12.8 11.6 10.4 9.3 8.3 7.3 6.4 5.8 5.2 4.6 4.0 3.5 3.0 2.5 2.2 2.0
69
Figure 26: IGCC CCS share along the efficient frontier at different levels of capital cost
with $20 (left) and $40/ton CO2 (right)
When CO2 price increases to $40/ton, IGCC CCS plays a more significant role.
From the baseline model, IGCC CCS replaces most of PC share when higher CO2 price is
imposed. When capital cost decreases, IGCC CCS starts to replace some of NGCC share
in the optimal portfolio with no significant change in nuclear share. However, when
capital cost increases, the share of IGCC CCS is replaced by NGCC and PC because
IGCC CCS is more expensive. Especially, when the capital cost increases by 30% (or
14% increase in total generation cost), there is almost no share of IGCC CCS in the
optimal portfolio.
Figure 27: IGCC share along the efficient frontier at different levels of capital cost with
$20 (left) and $40/ton CO2 (right)
IGCC is the dominated technology under the baseline model; there is no share of
IGCC in the optimal portfolio. When capital cost of IGCC is lowered by 20% (or 9%
decreases in total generation cost), IGCC becomes more competitive and replaces the
share of PC in the optimal portfolio. Under $20/ton CO2 price, IGCC replaces all PC in
the optimal portfolio; it acts like PC under the baseline model. When CO2 price increases
-30% -20% -10%
Baseline
10%
20%30%
0%
10%
20%
30%
40%
50%
60%
70%
Along the efficient frontier
-30% -20% -10%
Baseline
10%20%
30%0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Along the efficient frontier
-30% -20%
-10%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
Along the efficient frontier
-30% -20% -10%
0%
1%
2%
3%
4%
5%
6%
7%
Along the efficient frontier
70
Low CO2 price
High CO2 price
Baseline CCS cost
High CCS cost
High CCS cost
Baseline CCS cost
$40/ton CO2
$20/ton CO2
to $40/ton, it also replaces the tiny share of PC since the efficient portfolio is dominated
by NGCC, IGCC CCS and nuclear.
5. Sensitivity analysis of the CCS cost
In this analysis, we formulate 4 different scenarios of CO2 prices and CCS cost.
CO2 prices are low ($20/ton) and high ($40/ton). The CCS cost includes capture and
transportation and storage (T&S) costs. In this analysis, we assume no change in the
capture cost. The focus is on the uncertainty of T&S cost. We formulate 2 scenarios of
T&S cost; high and low. According to EPRI (2008), cost for CO2 transportation and
storage (T&S) for IGCC CCS with different types of coal and gasification technology is
in the range of $8.90 – 10.90/MWh. We set the baseline cost for CO2 T&S at $10/MWh
in the baseline model. The scenario with high CCS cost has the CO2 T&S cost at
$20/MWh.
Figure 28: Scenario analysis on CCS cost
The results from the scenarios with baseline CCS cost at 20 and 40 $/ton CO2
prices are presented in the previous section scenarios B3 and B4. Figure 29 shows the
technology mix of the portfolio on the efficient frontier under 4 scenarios.
71
(a) High CCS and Low CO2 price (b) High CCS and High CO2 price
(c) Baseline CCS and Low CO2 price (d) Baseline CCS and High CO2 price
Figure 29: Technology portfolios on the efficient frontier in 4 scenarios
Cost of CCS and CO2 are the important factors in this analysis. The optimal
portfolio changes significantly across these 4 scenarios. In the high CCS cost scenarios,
Figure 29a and b, share of IGCC CCS is small in both $20 and 40/ton of CO2 prices.
When price of CO2 is low (at $20/ton), PC has a large share in the portfolios especially
when cost of CCS is high, figure 29a. When price of CO2 increases to $40/ton, share of
PC decreases and is mostly replaced by NGCC.
When we compare models with low CO2 price at different CCS cost, shares of
NGCC along the efficient frontier change significantly. Large share of PC is replaced by
IGCC CCS. Some share of nuclear is also replaced. In figure 29a and c, the efficient
frontiers have about the same range in term of cost and standard deviation. It can be
obviously seen that the share of nuclear decreases significantly as CCS cost decreases. In
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
Nuclear
PC
IGCC CCSNGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
59.8 63.3 66.7 70.2 73.7 77.1 80.6 84.0 87.5 91.0 94.4 97.9 101.3
14.0 11.4 9.0 6.9 5.5 5.0 4.7 4.3 4.0 3.6 3.3 3.0 2.7 2.5 2.3 2.1 2.0
NuclearPC
IGCC CCSNGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.8 71.7 74.6 77.4 80.3 83.1 86.0 88.9 91.7 94.6 97.5 100.3 103.2
14.0 12.8 11.7 10.5 9.4 8.4 7.4 6.6 5.9 5.2 4.6 4.1 3.5 3.0 2.6 2.2 2.0
S.D.
Cost ($/MWh)
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
59.9 63.3 66.6 70.0 73.3 76.6 80.0 83.3 86.7 90.0 93.3 96.7 100.0
13.9 11.4 9.1 7.0 5.6 5.0 4.5 4.1 3.8 3.4 3.2 2.9 2.6 2.4 2.2 2.1 2.0
Nuclear
PCIGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.9 71.6 74.3 77.1 79.8 82.5 85.3 88.0 90.7 93.4 96.2 98.9 101.6
14.0 12.7 11.5 10.2 9.0 7.8 6.7 5.6 4.6 3.8 3.4 3.1 2.8 2.5 2.3 2.1 2.0S.D.
Cost ($/MWh)
72
addition, IGCC CCS gains higher share in the high cost and low variation portion of the
efficient frontier.
From figure 29d, low CCS cost and high CO2 price, NGCC, IGCC CCS and
nuclear play a significant role in the optimal portfolio. NGCC and IGCC CCS dominate
portfolios in the first half of the efficient frontier (low cost/high variation). In the second
half of the efficient frontier (high cost/low variation), IGCC CCS and nuclear have
significant share in the portfolios with small share of PC.
5. Bayesian analysis of power generation portfolio (applied BL model)
From the baseline model, we apply the Bayesian analysis to formulate the optimal
baseload generation portfolio. In this section, we show an example of the expression of
the posterior belief on the NGCC cost such that the investor forms his belief after
considering the the information on the baseline optimal portfolio mix, generation cost and
his expectation on the fuel market.
Example: The investor expects that cost of NGCC under the scenario with $40/ton
of CO2 will increase from $69/MWh to 90$ MWh due to high demand on natural gas.
From the baseline model with high CO2 price, NGCC is the technology that dominates
most part of the portfolio. The investor expresses different level of confidence (c) of his
belief on NGCC cost at the range. The optimal portfolio will be solved for 20, 50 and
80% level of confidence in the posterior belief. Cost ($/MWh) Baseline 20% CI 50% CI 80% CI
Nuclear 106.75 106.74 106.72 106.70 PC 93.42 93.51 93.64 93.77 PC CCS 103.68 97.51 97.44 97.37 IGCC 96.01 96.04 96.09 96.14 IGCC CCS 91.78 91.72 91.63 91.55 NGCC 68.82 73.06 79.41 85.76 NGCC CCS 72.36 78.04 86.55 95.07 Posterior belief S.D. - 28.05 14.03 7.01
Table 14: Power generation cost under different belief’s confidence
73
S.D.
Cost ($/MWh)Cost ($/MWh)
S.D.
Nuclear
PCIGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.9 71.6 74.3 77.1 79.8 82.5 85.3 88.0 90.7 93.4 96.2 98.9 101.6
14.0 12.7 11.5 10.2 9.0 7.8 6.7 5.6 4.6 3.8 3.4 3.1 2.8 2.5 2.3 2.1 2.0
Nuclear
PCIGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
73.1 75.4 77.7 80.1 82.4 84.8 87.1 89.5 91.8 94.1 96.5 98.8 101.2 103.5
18.82 16.44 14.09 11.79 9.58 7.54 5.84 4.85 4.30 3.81 3.39 3.07 2.87 2.80
Table 14 shows power generation cost from the baseline model and the model
with beliefs at different confidence levels. The value of NGCC cost that the investor
expects is $90/MWh. As confidence grows, the expected cost of NGCC is close to the
mean value. For example, at 80% confidence cost of NGCC is $85.76/MWh. In addition,
as shown at the bottom of the table, lower confidence translates to higher belief’s
standard deviation (variance). Costs of other technology also change when cost of NGCC
changes due to the correlation with NGCC cost. However, since the correlation of NGCC
and other technologies is low, costs of other technologies do not significantly change.
(a) baseline (b) 20% confidence
(c) 50% confidence (d) 80% confidence
Figure 30: Optimal portfolios under different view’s confidence
From figure 30, the optimal portfolios are solved under different confidence levels
in the belief. In this example, cost of NGCC is expected to increase to $90/MWh. Shapes
of the optimal portfolio changes in the direction toward using more NGCC when keeping
the portfolio cost fixed because the lower bound of the efficient portfolio frontier cost
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
79.4 81.3 83.1 85.0 86.8 88.7 90.5 92.4 94.2 96.1 97.9 99.8 101.6 103.5
17.17 14.55 11.99 9.54 7.29 5.51 4.68 4.25 3.85 3.49 3.19 2.98 2.84 2.79
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
85.8 87.2 88.6 90.0 91.5 92.9 94.3 95.7 97.2 98.6 100.0 101.4 102.9
15.35 11.73 8.34 5.59 4.60 4.27 3.96 3.67 3.41 3.19 3.02 2.89 2.81 2.78
74
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Baseline 20% CL 50% CL 80%
NuclearIGCC CCSNGCCPC
moves up as NGCC cost increases. Portfolio mix at $90/MWh is shown in figure 31
below.
Figure 31: Generation mix at $90/MWh
Higher natural gas cost shifts the lower bound cost of the efficient frontier. NGCC
cost is significantly higher but it is still the lowest cost technology. It is still the dominant
technology in the first half of the efficient frontier. Since this is under $40/ton of CO2
price, IGCC CCS plays significant role in this scenario. Nuclear and IGCC CCS replaces
NGCC shares as NGCC cost increases.
6. Portfolio with existing capacity
In the previous analysis, we assume all generation capacity in the portfolio is the
new capacity. In this section, we relax this assumption by assuming that there is some
existing capacity in the portfolio already. The planner’s decision is to choose the choice
of technology for the additional investment given that there is already existing capacity in
the portfolio.
In the model, there are 3 existing baseload capacity including NGCC, PC and
nuclear. EIA (2009c) estimates the average annual growth of generation capacity at 0.6%
during the next 3 decades; over the 15 year period, the cumulative growth is about 10%.
We assume that in the medium term (around 10 – 15 years) the system will need 10% of
new capacity. The existing capacity will be 90% of the future portfolio.
75
Nuclear (old)
Coal (old)
NGCC (old)
PC IGCC CCSNGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
39.9 40.1 40.3 40.5 40.6 40.8 41.0 41.2 41.4 41.6 41.7 41.9 42.1 42.3 42.5 42.7
$/MWh
3.34 3.20 3.07 2.96 2.85 2.75 2.67 2.63 2.62 2.60 2.59 2.58 2.57 2.55 2.55S.D.
Nuclear (old)
Coal (old)NGCC (old)
IGCC CCSNGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
43.3 43.5 43.6 43.8 43.9 44.0 44.2 44.3 44.5 44.6 44.8 44.9 45.0 45.2 45.3 45.5
$/MWh
3.42 3.35 3.28 3.21 3.15 3.08 3.02 2.96 2.90 2.84 2.78 2.73 2.68 2.63 2.58S.D.
Although the existing capacity is kept constant in the optimization process, the
result also depends on the existing mix. The correlation between the existing capacity and
the new capacity affects the optimal portfolio mix since the overall portfolio variance
calculation includes the weighted variance and covariance from the existing capacity. The
weight and variance of the existing capacity are fixed but the weighted covariance with
new capacity depends on the weight put on each new generation technology. The cost of
existing technology used in the calculation is only the variable cost since the investment
was already made. The cost series of the existing capacity are calculated from the
variable cost of the existing technology (for nuclear, PC and NGCC) in the baseline
model. We assume that variable cost of the existing capacity is 10% higher than the new
capacity due to lower efficiency. We will show the result of the optimal portfolio with 4
different mixes of the existing capacity.
a) Existing capacity with 30% nuclear, 50% PC and 10% NGCC
b) Existing capacity with 80% nuclear, 10% PC and 10% NGCC
Nuclear (old)
Coal (old)
NGCC (old)
NuclearPC IGCC CCSNGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
48.5 48.8 49.1 49.4 49.7 50.0 50.2 50.5 50.8 51.1 51.4 51.7 52.0 52.3 52.6 52.9
$/MWh
5.13 4.93 4.75 4.59 4.45 4.38 4.33 4.28 4.23 4.19 4.16 4.14 4.13 4.11 4.10S.D.
Nuclear (old)
Coal (old)
NGCC (old)
NuclearIGCC CCSNGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
60.0 60.2 60.5 60.7 61.0 61.2 61.4 61.7 61.9 62.1 62.4 62.6 62.8 63.1 63.3 63.5
$/MWh
5.13 5.01 4.90 4.78 4.67 4.56 4.46 4.35 4.26 4.16 4.15 4.14 4.12 4.11 4.10S.D.
76
Nuclear (old)
Coal (old)
NGCC (old)NuclearPC IGCC CCSNGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
51.1 51.4 51.7 51.9 52.2 52.5 52.8 53.1 53.4 53.7 54.0 54.3 54.6 54.8 55.1 55.4
$/MWh
5.08 5.01 4.95 4.89 4.83 4.78 4.73 4.69 4.65 4.61 4.58 4.55 4.53 4.50 4.48S.D.
Nuclear (old)
Coal (old)
NGCC (old)
NuclearIGCC CCSNGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
67.2 67.4 67.6 67.9 68.1 68.3 68.6 68.8 69.0 69.3 69.5 69.7 70.0 70.2 70.4 70.7
$/MWh
5.08 5.01 4.94 4.88 4.82 4.76 4.71 4.67 4.63 4.59 4.57 4.54 4.52 4.50 4.48S.D.
Nuclear (old)
Coal (old)
NGCC (old)
PC PC CCSIGCC CCSNGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
55.7 55.9 56.1 56.3 56.6 56.8 57.0 57.3 57.5 57.7 58.0 58.2 58.4 58.6 58.9 59.1
$/MWh
12.91 12.63 12.36 12.08 11.81 11.68 11.67 11.66 11.65 11.64 11.63 11.63 11.63 11.63S.D.
Nuclear (old)
Coal (old)
NGCC (old)
PC CCSIGCC CCSNGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
64.8 65.0 65.1 65.3 65.5 65.7 65.9 66.1 66.3 66.5 66.7 66.8 67.0 67.2 67.4 67.6
$/MWh
12.99 12.85 12.71 12.57 12.43 12.29 12.15 12.01 11.87 11.73 11.63 11.63 11.63 11.63
S.D.
c) Existing capacity with 10% nuclear, 80% PC and 10% NGCC
d) Existing capacity with 10% nuclear, 10% PC and 80% NGCC
Figure 32: Portfolio mix with existing capacity with $20 (left) and $40/ton CO2 (right)
The optimal portfolios of the new capacity shown in figure 32 are different due to
existing technology mix that varies in each case. However, the pattern of the technology
mix is similar to the baseline model. The portfolios with existing technology consisting of
30% nuclear, 50% PC and 20% NGCC (figure 32a) can approximately represent the
baseload technology mix in the current US power system. Like the baseline model,
NGCC is the dominant technology when portfolio cost is low and variation is high. There
are some shares of PC when CO2 price is low but they disappear when imposing higher
CO2 price. IGCC CCS plays key role when CO2 price is high. Nuclear dominates high
cost and low variation portfolios.
The optimal portfolios with existing capacity having nuclear 80%, PC and NGCC
10% (figure 32b) have no new nuclear capacity in the portfolio. Instead of having nuclear
77
as the technology to reduce portfolio variation, the optimal portfolios have IGCC CCS to
play this role. Since nuclear accounts for the majority of the existing portfolio, the
weighted covariance of old nuclear with other technology is large especially with the new
nuclear capacity. IGCC CCS has the lowest variation among the fossil fuel technology
and has lower cost than nuclear. Thus, in order to optimize the portfolio IGCC CCS is
selected for the high cost and low variation portfolios.
Similar effect of existing capacity can also be seen from the portfolio with
existing 80% PC, 10% nuclear and NGCC (figure 32c). Normally at $20/ton CO2 price
there are significant PC shares in the portfolio in other cases (also in the baseline model).
Since there are significant PC shares in the portfolio, more IGCC CCS and NGCC are
selected instead of PC to reduce overall variation. In addition, the mix of IGCC CCS and
NGCC can also lower the cost of portfolio; cost of PC is in the range between IGCC CCS
and IGCC.
Also, for the case with existing capacity 80% NGCC and 10% PC and nuclear
(figure 32d), there is small share of PC CCS instead of nuclear to reduce portfolio
variation. The mix of PC CCS and IGCC CCS play the role to reduce portfolio variation
in this case where NGCC has large share in the existing capacity. The correlation
between NGCC and PC CCS/IGCC CCS are lower than the correlation with nuclear.
Including both technologies can give lower portfolio variation than having nuclear while
cost of nuclear is in the range between these 2 technologies.
Examples of the optimal portfolio with various existing technology mixes indicate
the importance of correlation/covariance of existing capacity and new technology. In
general, the portfolio of the additional investment looks similar to the one in the baseline
model. However, share of some technologies can be different depending on the mix of
existing capacity.
78
Conclusion
In this study, we present the methodology to apply the mean variance portfolio
theory to solve for the optimal power generation portfolio. Rather than choosing a
winning technology, we propose power generation planning in term of the portfolio. The
baseload generation is the focus of the study because it accounts for most of electricity
generation and cost of the power system.
Different technologies play different roles in the portfolio (power system). The
nuclear power plant has high capital cost and low variable cost compared with other
technologies. The generation cost from nuclear is high but has low variation. In addition,
power generation cost from nuclear is not affected by cost of CO2 regulation. NGCC is
the technology with low cost but high variation in cost since the majority of the
generation cost of the natural gas plant is fuel cost. Variation in natural gas price
significantly affects variation in NGCC generation cost.
We solved the efficient portfolio frontier in term of generation cost and variation
in generation cost. Models with different CO2 prices show significantly different
technology mixes along the portfolio frontiers. Since one of the key factors that
determines the optimal mix is the order of the cost. Increase in CO2 price changes the
relative cost or order among all technologies. The change in CO2 pricelargely affects the
high CO2 emission technology such as PC and IGCC. When the CO2 price increases,
NGCC IGCC with CCS replace most of the PC share in the portfolio. The baseline
portfolio mix shows that cost of CO2 at $20/ton is not high enough to encourage
investment in clean coal technology (IGCC CCS) which can reduce both cost and
variation in cost and importantly CO2 emission.
In addition, the model is analyzed under different fuel price. The first analysis
separate the time period into “stable price” and “volatile price” periods. The results from
these 2 periods are different due to differences in average fuel price and correlation
structure. The second analysis assumes different scenarios of natural gas price. The result
shows that if natural gas price significantly increases from the baseline value, portfolio
planned using the baseline cost will impose additional cost in the future. The additional
cost can be reduced if the planning is based on more risk aversion preference.
79
The model is also analyzed with different capital cost levels since most reported
cost is in range. Changes in capital cost have more effects on technology with higher
capital intensive. The result from model where all technologies capital cost change in the
range ±30% shows different portfolio mix from the baseline model but significant change
occurs to few technologies such as PC and IGCC CCS. Significant change occurs when
the cost order of technology at the boundary of the efficient portfolio (for example NGCC
and nuclear) changes.
We also show an example applying the Bayesian analysis to power generation
portfolio. This approach has been used in finance so called “Black and Litterman” model.
With this model, the investor can express his belief on one or more technology cost with
the level of confidence in the belief. We show an example of different confidence levels
that can lead to significantly different power generation portfolios.
Our model has limitation in accounting for all types of risk in the power system.
Risks, for example power plant outage and other environmental regulations, are not
included in the model. However, this study can give portfolio selection criteria and policy
implication regarding to investment under uncertainty in CO2 and fuel prices. Especially,
it underlines an importance of planning in term of portfolio. If most of the new generation
capacity is NGCC, as most utilities plan today, it could impose significant cost in the
future when natural gas price increases from the scenario they plan.
80
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83
Appendix
A. Data and Assumptions
The key variable in this study is power generation cost ($/MWh). There are 2
major components of cost; fixed and variable cost. In our study, we assume that all
generating capacity in the system is new capacity. To calculate the fixed cost per unit, we
need the following data; the total plant cost7, capacity factor, economic lifetime of the
power plan and discount rate. The investment cost that we use is the total plant cost
assuming that the power plant is built overnight and all costs are evaluated in the present
value term. Total amount of power generated each year is calculated from the capacity
factor. Using the annual fixed cost and output, we can find the fixed cost per MWh. The
detail on the sources of data is presented later in this section.
To calculate the variable cost, we use the data on fuel price, O&M cost, heat rate
and CO2 emission rate (per MWh). The fuel cost for the fossil fuel plant is calculated
from the fuel cost ($/Btu) and heat rate8 (Btu/kWh). For the nuclear plant, the calculation
for fuel cost is different from the fossil fuel power plant. We use the approach in “The
Economics of the Nuclear Fuel Cycle”, Nuclear Energy Agency (1994) and the nuclear
fuel cost calculator from the WISE Uranium project (http://www.wise-
uranium.org/index.html). This requires the data on uranium, conversion, enrichment and
fabrication prices. In addition, the CO2 price is the part of the variable cost. Different
types of fossil fuel plant emit different amount of CO2 per MWh. Thus, they have
different cost of CO2 depending on their emission rate. The variable cost per MWh is the
sum of fuel, O&M and CO2 price (for fossil fuel plant). Mean, correlation and the
covariance matrix are calculated from the series of generation cost.
7 DOE (1999) defines “the total plant cost” as the capital cost including all construction related costs such as equipments, material, labor and contingencies. 8 According to the definition from Energy Information Administration (EIA), “heat rate is a measure of generating station thermal efficiency commonly stated as Btu per kilowatt hour” (EIA, http://www.eia.doe.gov/glossary/glossary_h.htm).
84
Total plant
cost a ($/kW)
Heat rate b
(Btu/kWh)
Capacity
factor (%)
CO2 emission d
(ton/MWh)
Economic
life (years)
Nuclear 6,000e NA c 90 - 40
PC 1900 9,000 80 1.00 40
PC CCS 3,150 12,500 80 0.10 40
IGCC 2,200 8,850 80 0.90 25
IGCC CCS 3,050 10,700 80 0.09 25
NGCC 550 7,000 80 0.45 25
NGCC CCS 1,300 8,600 80 0.045 25
Table A1: Assumptions on generation cost
Note:
a) The total plant cost is estimated based on many sources for example EPRI (2008),
EIA (2008a), NETL (2007) and Synapse (2008). However, currently, investment
cost is increasing and there is no consensus on the number especially for nuclear
and IGCC plants. The cost used in this study is from the median value of the
reported cost.
b) The heat rate data is estimated based on many sources such as EIA (2008b), EPRI
(2008), NETL (2007) and IECM (Integrated Environmental Control Model).
c) The heat rate from the nuclear plant is calculated from the approach in “The
Economics of the Nuclear Fuel Cycle”, Nuclear Energy Agency (1994) and the
nuclear fuel cost calculator from the WISE Uranium project (http://www.wise-
uranium.org/index.html).
d) The CO2 emission rate is estimated based on data from eGrid (2006) and EPRI
(2008).
e) Nuclear total plant cost reported in Synapse (2008) ranges from $3,600-
8,081/kW. Cost at $6,000/kW is selected for the study. It is around the median of
the reported range. This cost is higher than other estimate such as EIA (2008b).
However, the realized cost of the nuclear plant tends to be higher than the initial
estimate. EIA (1994) showed that during 1966-1977 the realized overnight cost of
nuclear power plants were 2-3.5 times of the initial estimate.
85
Fuel cost
The fossil fuel cost data is from EIA (2009a) “Cost of Fossil-Fuel Receipts at
Electric Generating Plants”. This is the monthly data in $/MBtu unit.
Uranium: Monthly uranium price data is from the Cameco Corp.
(http://www.cameco.com/marketing/uranium_prices_and_spot_price/longterm_complete
_history/).
O&M cost
The O&M cost data of the existing technology is from EIA (2009b), “Average
Power Plant Operating Expenses for Major U.S. Investor-Owned Electric Utilities”. The
data is from 1995 – 2009. The data from 1990-1994 is estimated by using the average
growth rate. The O&M cost for IGCC and IGCC CCS are estimated from EPRI (2008).
CO2 price
The CO2 regulation price in our study is the simulated data with a certain mean
and variance. The CO2 price is simulated from normal distribution with mean $20 and
40/ton with standard deviation 5. The study by Roques et al. (2007) simulated the CO2
price at mean of ₤40/ton and standard deviation of 10.
86
B. Generation technology portfolio: All load types
The first step in analyzing portfolio for all load types is to categorize technology
from load serving characteristic and derive power generation cost. Previous studies do
not take into account the load curve and capacity factor of the plants serving different
load portions. For example, a baseload plant has a higher capacity factor than the plants
serving the intermediate load or peak load.
Figure B1: PJM load duration curve divided to 3 parts
From figure B1, the load duration curve is divided into 3 types of load; baseload,
intermediate and peak load. The percentages by amount of power (MWh) of baseload,
intermediate and peak load are about 78, 18 and 4% respectively. In addition, the shares
in terms of capacity (MW) of the plants serving each load are 44, 18 and 38% for the
base, intermediate and peak load respectively. In addition, we need to define the capacity
factor for the technology serving each load. The baseload plant has a capacity factor
around 80-90% while those of intermediate and peak load plants are 50-60% and 5-10%
respectively. The capacity factor is important for the calculation of the fixed cost per
MWh.
To solve the portfolio optimization problem, we set the “load weight” in term of
energy (MWh) for each load type. For example, the load weight for the base,
intermediate and peak load are 78, 18, and 4% respectively. In each load category, there
is a mix of fuel-technology plants serving the load. While each plant has some flexibility,
we assume that each plant can only serve the load it was designed for. Nuclear and coal
0
20000
40000
60000
80000
100000
120000
140000
160000
1 514 1027 1540 2053 2566 3079 3592 4105 4618 5131 5644 6157 6670 7183 7696 8209 8722
Hours
MW
Baseload
Intermediate load
Peak load
0
20000
40000
60000
80000
100000
120000
140000
160000
1 514 1027 1540 2053 2566 3079 3592 4105 4618 5131 5644 6157 6670 7183 7696 8209 8722
Hours
MW
Baseload
Intermediate load
Peak load
87
plants serve baseload. (Some old coal plants are also cycled for serving intermediate
load.) A natural gas combined cycle (NGCC) serves base and intermediate load. A simple
gas turbine (GT) and diesel plants which can be ramped up and down quickly serve peak
demand.
Power generation investment has a lumpy nature that may create a discontinuity
in portfolio analysis. In this study, power generation capacity is assumed to be perfectly
divisible. The planner solves the optimal risk-cost portfolio from the following quadratic
programming problem. Additional constraints are imposed on the weight of each load
type. In addition, all weights are greater than or equal to zero (similar to a no short sale
constraint in the conventional mean-variance portfolio model).
Min 1 1
12
N N
i j iji j
w w σ= =∑∑
Subject to: 1
1N
ii
w=
=∑ or WB + WI +WP = 1
1
N
i ii
w c μ=
=∑
,
bn
B k Bk
w W=∑
,
in
I k Ik
w W=∑
,
pn
P k Pk
w W=∑
0iw ≥ for all I = 1,…,N
iw is the portfolio weight of technology i (N technologies in total). μ is a specific
value of portfolio cost. ijσ is the covariance of technology i and j. N = nB + nI + nP where
nB, nI and nP are the number of technology serving base, intermediate and peak load
respectively. WB, WI and WP are weights in term of energy (MWh) of base, intermediate
and peak load respectively.
88
C. Analysis of nuclear plant shutdown
Nuclear plants experienced extensive shutdowns for safety or inspection in the
decade of 1970s, since the technology and safety measures were not fully developed.
However, we expect that the future nuclear power plant will have less evidence of
shutdown for safety because the technology is more developed and improved. In this
analysis, we formulate the optimal portfolio under the situation that some capacity of the
nuclear power plant is shut down for some periods. The shutdown is not permanent and
for maintenance or regulatory inspection.
Prior to the decision on the portfolio mix, the planner forms an expectation about
the possibility of the shutdown by a certain period of time. We assume that the shutdown
affects the overall capacity of the plant. When the plant is shut down, its overall capacity
factor decreases. Decrease in capacity factor depends on the length of shutdown; the long
period of shutdown leads to low capacity factor. For the nuclear plant that is shut down,
the maintenance cost is assumed to be higher than the normal plant. In addition, the
variation of the maintenance cost of the shutdown plant is also higher.
In this analysis, we test few cases of nuclear plant shutdown by varying the
probability and loss of capacity factor. The probabilities of shutdown are set at 10 and
20% and the loss of capacity is set at 10 and 20%. Note that the baseline assumption sets
capacity factor of the nuclear plant at 90%. At 10% probability of shutdown, the expected
generation costs from nuclear are $108.3 and $109.6/MWh for capacity factor loss 10 and
20% respectively. Also at 20% probability of shutdown, the expected generation costs
from nuclear are $109.7 and $112.6/MWh for capacity factor loss 10 and 20%
respectively. In addition, for all cases the variation of the nuclear plant cost increases due
to the change in maintenance cost but not in a high magnitude.
The portfolio mix of each scenario is shown in figure C1. Since the shutdown
increases cost of the nuclear plant, it is still the highest cost-lowest variation technology;
the variation in cost does not increase significantly. The optimal portfolios from all
scenarios look similar to the baseline portfolio.
89
a) 10% shutdown probability and 10% loss in capacity factor
b) 10% shutdown probability and 20% loss in capacity factor
c) 20% shutdown probability and 10% loss in capacity factor
d) 20% shutdown probability and 20% loss in capacity factor
Figure C1: Portfolio mix of all scenario at $20 (left) and $40/ton CO2 (right)
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
59.8 63.2 66.7 70.1 73.5 76.9 80.3 83.7 87.1 90.6 94.0 97.4 100.8
14.0 11.5 9.1 7.0 5.5 5.0 4.5 4.1 3.7 3.4 3.1 2.9 2.6 2.4 2.2 2.1 2.0
Nuclear
PCIGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.8 71.7 74.5 77.3 80.1 83.0 85.8 88.6 91.4 94.3 97.1 99.9 102.7
14.0 12.7 11.4 10.1 8.9 7.6 6.5 5.3 4.4 3.7 3.3 3.0 2.7 2.5 2.2 2.1 2.0
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
NuclearPC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
59.8 63.3 66.8 70.4 73.9 77.4 80.9 84.4 87.9 91.4 94.9 98.4 101.9
14.0 11.4 9.0 6.8 5.5 4.9 4.4 4.0 3.7 3.4 3.1 2.8 2.6 2.4 2.2 2.1 2.0
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.8 71.7 74.6 77.5 80.4 83.3 86.2 89.1 92.0 94.9 97.8 100.7 103.7
14.0 12.7 11.3 10.0 8.7 7.5 6.3 5.2 4.2 3.6 3.2 2.9 2.7 2.4 2.2 2.1 2.0
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
NuclearPC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
59.8 63.3 66.8 70.3 73.8 77.3 80.8 84.3 87.8 91.3 94.8 98.3 101.8
14.0 11.4 9.0 6.9 5.5 4.9 4.4 4.0 3.7 3.4 3.1 2.8 2.6 2.4 2.2 2.1 2.0
Nuclear
PCIGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.8 71.7 74.6 77.5 80.4 83.3 86.2 89.2 92.1 95.0 97.9 100.8 103.7
14.0 12.7 11.3 10.0 8.7 7.5 6.3 5.2 4.2 3.6 3.2 2.9 2.7 2.4 2.2 2.1 2.0
S.D.
Cost ($/MWh)
S.D.
Cost ($/MWh)
NuclearPC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
59.8 63.5 67.1 70.8 74.4 78.0 81.7 85.3 89.0 92.6 96.3 99.9 103.5
14.0 11.3 8.8 6.6 5.3 4.8 4.3 3.9 3.6 3.3 3.0 2.8 2.6 2.4 2.2 2.1 2.1
Nuclear
PC
IGCC CCS
NGCC
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
68.8 71.9 74.9 78.0 81.0 84.1 87.1 90.2 93.2 96.3 99.3 102.4 105.4
14.0212.3010.59 8.92 7.30 5.78 4.46 3.57 3.18 2.86 2.57 2.33 2.16 2.06
90
The shapes of portfolio mix along the frontier of all scenarios are similar. Figure
C2 shows the plot of the share of nuclear along the efficient frontier by normalizing the
frontier on the horizontal axis. At each level of CO2 price, the line graph shows that there
is no significant difference in the share of nuclear along the efficient frontier.
Figure B2: Share of nuclear in all scenarios at $20 (left) and $40/ton CO2 (right)
0%
10%
20%
30%
40%
50%
60%
70%
80%
Along the efficient frontier0%
10%
20%
30%
40%
50%
60%
70%
80%
Along the efficient frontier